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<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">p0</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>reconsider </b><font color="Maroon">Pt</font> =  <a href="scpqsort.html#K1" target="_self">Partition</a>  as  <a href="scmpds_4.html#V3">shiftable</a> <a href="scmpds_5.html#V3">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a> ;<br/>
<b>set </b><font color="Maroon">pn</font> = <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>;<br/>
<b>set </b><font color="Maroon">l1</font> = <a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">l2</font> =  <a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">l3</font> = <a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">l4</font> = <a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">l5</font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">l6</font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4;<br/>
<b>set </b><font color="Maroon">l7</font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4;<br/>
<b>set </b><font color="Maroon">l8</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">l9</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1;<br/>
<b>set </b><font color="Maroon">l0</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2;<br/>
<b>set </b><font color="Maroon">lb</font> =  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">L5</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>;<br/>
<b>set </b><font color="Maroon">TR</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">IF4</font> =  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">WB4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">WH4</font> =  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<i><font color="Green">E42</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmp_gcd.html#T8">SCMP_GCD:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmp_gcd.html#T8">SCMP_GCD:8</a></i>
<br/>.= 
<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i/>
;<br/>
<i><font color="Green">E58</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T9">SCMP_GCD:9</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_6.html#T79">SCMPDS_6:79</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T6">SCMPDS_5:6</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <a href="scpqsort.html#K1" target="_self">Partition</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <a href="scpqsort.html#K1" target="_self">Partition</a> </span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
2 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K1">+</a> 38</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T9">SCMP_GCD:9</a></i>
<br/>.= 
51
<b>by </b><i/>
;<br/>
<b>set </b><font color="Maroon">m1</font> = <a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">m2</font> = <a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1;<br/>
<b>set </b><font color="Maroon">m3</font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">m4</font> = <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">M4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>;<br/>
<b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_4.html#T45">SCMPDS_4:45</a></i>
<br/>.= 
4 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
4 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">51 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3"><i><font color="Green">Lemma45</font></i></a>, <a class="ref" href="scmpds_8.html#T17">SCMPDS_8:17</a></i>
<br/>.= 
57

;<br/>

<b>assume </b><a NAME="E5:46"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">p0</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 ;<br/>

<b>set </b><font color="Maroon">s1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">a</font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<a NAME="E6:46"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:46"/>
7 <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E9:46"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E10:46"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E11:46"/><i><font color="Green">E64</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font>, <font color="Olive">m1</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> &amp; <font color="Olive">m1</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="nat_1.html#K1">+</a> 1 holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> 2 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:46_4"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/>

<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t3</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t4</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t5</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t6</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<a NAME="E2:46_4"/>
<font color="Maroon">m1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E3:46_4"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:46_4"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:46_4"/><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E6:46_4"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 3
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:46_4"/><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<b>then </b><i><font color="Green">E74</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>

;<br/>
<div><i><font color="Green">E75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 ;<br/><a NAME="E2:46_4_2"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E10:46_4"/><b>then </b><i><font color="Green">E76</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E11:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E12:46_4"/><b>then </b><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E13:46_4"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E14:46_4"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a></i>;<br/>
<a NAME="E15:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
;<br/>
<a NAME="E16:46_4"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a></i>;<br/>
<i><font color="Green">E84</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<i><font color="Green">E85</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>
<div><i><font color="Green">E102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_5"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:46_4_5"/><b>then </b><i><font color="Green">E135</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46_4"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E20:46_4"/><b>then </b><i><font color="Green">E136</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E21:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E22:46_4"/><b>then </b><i><font color="Green">E137</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E23:46_4"/><i><font color="Green">E138</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E24:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E25:46_4"/><b>then </b><i><font color="Green">E139</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E67</font></i></a></i>;<br/>
<i><font color="Green">E140</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46_4"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a></i>
;<br/>
<a NAME="E27:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E28:46_4"/><b>then </b><i><font color="Green">E141</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E1:46_4"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E67</font></i></a></i>;<br/>
<i><font color="Green">E142</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/>
<div><i><font color="Green">E143</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_8"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 ;<br/><a NAME="E2:46_4_8"/><b>then </b><i><font color="Green">E144</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E31:46_4"/><b>then </b><i><font color="Green">E145</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E32:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E33:46_4"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E34:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E35:46_4"/><b>then </b><i><font color="Green">E147</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<a NAME="E36:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E37:46_4"/><b>then </b><i><font color="Green">E162</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46_4"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<i><font color="Green">E163</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46_4"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46_4"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E67</font></i></a>, </i>
;<br/>
<a NAME="E39:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E40:46_4"/><b>then </b><i><font color="Green">E165</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E7:46_4"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E75</font></i></a></i>;<br/>
<i><font color="Green">E166</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_4"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>
<div><i><font color="Green">E167</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_11"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_11"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:46_4_11"/><b>then </b><i><font color="Green">E168</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E16:46_4"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_4"><i><font color="Green">E84</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E43:46_4"/><b>then </b><i><font color="Green">E170</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46_4"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E44:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E45:46_4"/><b>then </b><i><font color="Green">E171</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E12:46_4"><i><font color="Green">E77</font></i></a>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E46:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E47:46_4"/><b>then </b><i><font color="Green">E172</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E173</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E16:46_4"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/>
<a NAME="E49:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E50:46_4"/><b>then </b><i><font color="Green">E174</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E13:46_4"><i><font color="Green">E80</font></i></a>, </i>;<br/>
<a NAME="E51:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E52:46_4"/><b>then </b><i><font color="Green">E175</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E14:46_4"><i><font color="Green">E81</font></i></a>, </i>;<br/>
<i><font color="Green">E176</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E18:46_4"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/>
<div><i><font color="Green">E179</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_14"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_14"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 ;<br/><a NAME="E2:46_4_14"/><b>then </b><i><font color="Green">E182</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E55:46_4"/><b>then </b><i><font color="Green">E183</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E17:46_4"><i><font color="Green">E84</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E56:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E57:46_4"/><b>then </b><i><font color="Green">E184</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E18:46_4"><i><font color="Green">E85</font></i></a>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E58:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E59:46_4"/><b>then </b><i><font color="Green">E185</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scpqsort.html#T3" target="_self">Th3</a>, </i>;<br/>
<a NAME="E60:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E61:46_4"/><b>then </b><i><font color="Green">E186</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E187</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/>
<a NAME="E63:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E64:46_4"/><b>then </b><i><font color="Green">E188</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E65:46_4"/><i><font color="Green">E189</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E190</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_4_16"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_16"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><a NAME="E2:46_4_16"/><b>then </b><i><font color="Green">E191</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E67:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
;<br/>

<a NAME="E69:46_4"/>
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E70:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<a NAME="E71:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E72:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, </i>;<br/>

<a NAME="E73:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E74:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i>, </i>;<br/>

<a NAME="E75:46_4"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E76:46_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_4_18"/><i><font color="Green">E192</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> )
 ;<br/><a NAME="E2:46_4_18"/><b>then </b><i><font color="Green">E193</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_4_18"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:46_4_18"/><i><font color="Green">E196</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:46_4_18"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E102</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpqsort.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46_4"><i><font color="Green">E75</font></i></a>, , <a class="txt" href="scpqsort.html#E19:46_4"><i><font color="Green">E102</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E4:46_4"><i><font color="Green">E67</font></i></a>, , <a class="ref" href="scpqsort.html#T4" target="_self">Th4</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, , </i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E12:46"/><i><font color="Green">E198</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m1</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t3</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_5"/><i><font color="Green">E199</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> )
 ;<br/>

<a NAME="E2:46_5"/>
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E3:46_5"/><b>then </b><i><font color="Green">E200</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:46_5"/><i><font color="Green">E201</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E5:46_5"/><i><font color="Green">E202</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E6:46_5"/><i><font color="Green">E203</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E7:46_5"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E8:46_5"/><b>then </b><i><font color="Green">E204</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E9:46_5"/>
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E10:46_5"/><b>then </b><i><font color="Green">E205</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E206</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E12:46_5"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E13:46_5"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>then </b><i><font color="Green">E207</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E15:46_5"/><i><font color="Green">E208</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E16:46_5"/><b>then </b><i><font color="Green">E209</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_5_5"/><i><font color="Green">E210</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 )
 ;<br/><a NAME="E2:46_5_5"/><b>then </b><i><font color="Green">E211</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E3:46_5_5"/><i><font color="Green">E212</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,4
 <b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E13:46"/><i><font color="Green">E213</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m1</font>, <font color="Olive">md</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">md</font> &amp; <font color="Olive">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Olive">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Olive">t</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">md</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">lPt</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_6"/><i><font color="Green">E214</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font> &amp; <font color="Maroon">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:46_6"/><b>then </b><i><font color="Green">E215</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:46_6"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_6"/><b>then </b>
( <font color="Maroon">Pt</font> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp; <font color="Maroon">Pt</font> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E5:46_6"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<b>hence </b><a NAME="E6:46_6"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T9">SCPISORT:9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:46"/><i><font color="Green">E216</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font>, <font color="Olive">m1</font>, <font color="Olive">md</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">n4</font> being  <a href="int_1.html#NM1">Integer</a><br/> for <font color="Olive">f1</font>, <font color="Olive">f2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> &amp; <font color="Olive">m1</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">md</font> &amp; <font color="Olive">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">n4</font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">n4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">n4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> &amp; <font color="Olive">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Olive">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Olive">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Olive">md</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">n4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m1</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) &amp; <font color="Olive">f1</font>,<font color="Olive">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp;  ex <font color="Olive">m4</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">m4</font> &amp; <font color="Olive">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n4</font> &amp; <font color="Olive">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">m4</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">md</font> ) or ( <font color="Olive">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">md</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n4</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">f2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>







<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">lPt</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t4</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">tp</font> =  <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:46_7"/><i><font color="Green">E217</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font> &amp; <font color="Maroon">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">n4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">n4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">n4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/>

<b>assume </b><a NAME="E2:46_7"/><i><font color="Green">E218</font></i>: 
( <font color="Maroon">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<b>assume </b><a NAME="E3:46_7"/><i><font color="Green">E219</font></i>: 
( <font color="Maroon">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<a NAME="E4:46_7"/><i><font color="Green">E220</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 &amp; <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:46_7"/><i><font color="Green">E221</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E6:46_7"/><i><font color="Green">E222</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n4</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:46_7"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_1"/><i><font color="Green">E224</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><a NAME="E2:46_7_1"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_7_1"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_1"/><b>then </b><i><font color="Green">E225</font></i>: 
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:46_7"/><b>then </b><i><font color="Green">E226</font></i>: 
<font color="Maroon">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">f4</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E11:46_7"/><i><font color="Green">E227</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f4</font> holds <br/><font color="Maroon">f4</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">i</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/>
<a NAME="E12:46_7"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">f4</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E13:46_7"/><b>then </b><i><font color="Green">E229</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> &amp; <font color="Maroon">f1</font>,<font color="Maroon">f4</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  )
 
<b>by </b><i>, , , <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E2:46"><i><font color="Green">E42</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">m4</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E15:46_7"/><i><font color="Green">E230</font></i>: 
( <font color="Maroon">m4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> &amp; <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m4</font> &amp; <font color="Maroon">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 <b>by </b><i>, , , <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scpqsort.html#E2:46"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E16:46_7"/><i><font color="Green">E231</font></i>: 
( <font color="Maroon">Pt</font> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp; <font color="Maroon">Pt</font> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i>, , <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, </i>;<br/>
<a NAME="E17:46_7"/><b>then </b><i><font color="Green">E232</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<a NAME="E18:46_7"/><i><font color="Green">E233</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>;<br/>
<i><font color="Green">E234</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<font color="Maroon">m1</font>
<b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
;<br/>
<a NAME="E20:46_7"/><b>then </b><i><font color="Green">E235</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> 2 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E21:46_7"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">m1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E22:46_7"/><b>then </b><i><font color="Green">E237</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E23:46_7"/><i><font color="Green">E238</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E24:46_7"/><b>then </b><i><font color="Green">E240</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E25:46_7"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E26:46_7"/><i><font color="Green">E243</font></i>: 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E27:46_7"/><b>then </b><i><font color="Green">E244</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E28:46_7"/><b>then </b><i><font color="Green">E245</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>thus </b><a NAME="E29:46_7"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>;<br/>

<b>thus </b><a NAME="E30:46_7"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>;<br/>

<a NAME="E31:46_7"/>
( <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><font color="Maroon">md</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><br/>

<a NAME="E33:46_7"/><i><font color="Green">E246</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E34:46_7"/><i><font color="Green">E247</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<a NAME="E35:46_7"/><b>then </b><i><font color="Green">E248</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E36:46_7"/><i><font color="Green">E249</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E37:46_7"/>
( <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>hence </b><font color="Maroon">n4</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_5"/><i><font color="Green">E250</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> )
 ;<br/><a NAME="E2:46_7_5"/><b>then </b><i><font color="Green">E251</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 7
 <b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E3:46_7_5"/><i><font color="Green">E252</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_7_5"/><i><font color="Green">E253</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E5:46_7_5"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:46_7_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E7:46_7_5"/><b>then </b><i><font color="Green">E254</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:46_7_5"/><i><font color="Green">E256</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, , , , , <a class="ref" href="scpqsort.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
;<br/></div>
<b>end;</b></div>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_6"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:46_7_6"/><b>then </b><i><font color="Green">E325</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:46_7_6"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_7_6"/><b>then </b><i><font color="Green">E326</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_7_6"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:46_7_6"/><b>then </b><i><font color="Green">E327</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, , , , , <a class="ref" href="scpqsort.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<font color="Maroon">f4</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E41:46_7"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>

<b>take </b>
<font color="Maroon">m4</font>
;<br/>

<b>thus </b><a NAME="E42:46_7"/>
( <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m4</font> &amp; <font color="Maroon">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> )
 <b>by </b><i>, , </i>;<br/>

<a NAME="E43:46_7"/><i><font color="Green">E371</font></i>: 
<font color="Maroon">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E44:46_7"/><i><font color="Green">E372</font></i>: 
<font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E45:46_7"/><i><font color="Green">E373</font></i>: 
<font color="Maroon">m4</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<b>thus </b><font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i>, , <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/>

<b>thus </b><font color="Maroon">m4</font> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, , <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_9"/><i><font color="Green">E374</font></i>: 
( <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m4</font> )
 ;<br/><a NAME="E2:46_7_9"/><b>then </b><i><font color="Green">E375</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_9"/><i><font color="Green">E376</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><i><font color="Green">E377</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , , , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, , , , , <a class="ref" href="scpqsort.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><b>hence </b><a NAME="E6:46_7_9"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, , </i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_10"/><i><font color="Green">E378</font></i>: 
( <font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> )
 ;<br/><a NAME="E2:46_7_10"/><b>then </b><i><font color="Green">E379</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_10"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">md</font>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_10"/><b>then </b><i><font color="Green">E380</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><i><font color="Green">E381</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , , , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, , , , , <a class="ref" href="scpqsort.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
;<br/><b>hence </b><a NAME="E7:46_7_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, , , </i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_7_11"/><i><font color="Green">E382</font></i>: 
( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> ) or ( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) )
 ;<br/><div><i><font color="Green">E383</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_7_11_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_7_11_1_1"/>
( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> ) or ( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1_1"><b>suppose </b></a><a NAME="E1:46_7_11_1_1_1"/><i><font color="Green">E384</font></i>: 
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_7_11_1_1_1"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; ( <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> ) )
 <b>by </b><i>, </i>;<br/><a NAME="E3:46_7_11_1_1_1"/>
<font color="Maroon">md</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_7_11_1_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_7_11_1_1_2"><b>suppose </b></a><a NAME="E1:46_7_11_1_1_2"/><i><font color="Green">E385</font></i>: 
( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/><div class="add"><a NAME="E2:46_7_11_1_1_2"/>
<font color="Maroon">n4</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">md</font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_7_11_1_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">md</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_7_11_1_1_2"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><a NAME="E5:46_7_11_1_1_2"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> or <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> )
 <b>by </b><i>, , </i>;<br/><b>thus </b><a NAME="E6:46_7_11_1_1_2"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:46_7_11"/><b>then </b><i><font color="Green">E386</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_7_11"/><b>then </b><i><font color="Green">E387</font></i>: 
( <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 4 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T7">SCPISORT:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, , , , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">Pt</font>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, , </i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E15:46"/><i><font color="Green">E388</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m</font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:46_8"/><i><font color="Green">E389</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 ;<br/>

<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<a NAME="E2:46_8"/><i><font color="Green">E390</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E3:46_8"/><i><font color="Green">E391</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E4:46_8"/><i><font color="Green">E392</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E5:46_8"/><i><font color="Green">E393</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E6:46_8"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E7:46_8"/><b>then </b><i><font color="Green">E394</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E8:46_8"/>
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E9:46_8"/><b>then </b><i><font color="Green">E395</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E396</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E11:46_8"/>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E12:46_8"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>then </b><i><font color="Green">E397</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E14:46_8"/><i><font color="Green">E398</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_8_4"/><i><font color="Green">E399</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2
 ;<br/><a NAME="E2:46_8_4"/><b>then </b><i><font color="Green">E400</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E3:46_8_4"/><i><font color="Green">E401</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i>, , <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E16:46"/><i><font color="Green">E402</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font>, <font color="Olive">md</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m</font> &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">md</font> &amp; ( <font color="Olive">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 or <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">md</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 ) holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Olive">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Olive">t</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">md</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>assume </b><a NAME="E1:46_9"/><i><font color="Green">E403</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font> &amp; ( <font color="Maroon">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 or <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 ) )
 ;<br/>

<a NAME="E2:46_9"/><b>then </b><i><font color="Green">E404</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:46_9"/><i><font color="Green">E405</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_9"/><b>then </b><i><font color="Green">E406</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_9_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1_1"><b>suppose </b></a><a NAME="E1:46_9_1_1"/><i><font color="Green">E407</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:46_9_1_1"/><i><font color="Green">E408</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><a NAME="E3:46_9_1_1"/><i><font color="Green">E409</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 <b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E4:46_9_1_1"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_9_1_1"/><b>then </b><i><font color="Green">E410</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:46_9_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E7:46_9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:46_9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E9:46_9_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 <b>by </b><i>, , , <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E10:46_9_1_1"/><b>then </b>
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_6.html#T82">SCMPDS_6:82</a></i>;<br/><b>hence </b><a NAME="E11:46_9_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_9_1_2"><b>suppose </b></a><a NAME="E1:46_9_1_2"/><i><font color="Green">E411</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:46_9_1_2"/>
(  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/><a NAME="E3:46_9_1_2"/><b>then </b>
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_6.html#T83">SCMPDS_6:83</a></i>;<br/><b>hence </b><a NAME="E4:46_9_1_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E17:46"/><i><font color="Green">E412</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font>, <font color="Olive">m1</font>, <font color="Olive">md</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">n4</font> being  <a href="int_1.html#NM1">Integer</a><br/> for <font color="Olive">f1</font>, <font color="Olive">f2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> &amp; <font color="Olive">m1</font> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">md</font> &amp; <font color="Olive">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">n4</font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">n4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">n4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> &amp; <font color="Olive">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Olive">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Olive">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Olive">md</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive">n4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m1</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) &amp; <font color="Olive">f1</font>,<font color="Olive">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp;  ex <font color="Olive">m4</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">m4</font> &amp; <font color="Olive">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n4</font> &amp; <font color="Olive">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Olive">m4</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">md</font> ) or ( <font color="Olive">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">md</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n4</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">f2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>







<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>assume </b><a NAME="E1:46_10"/><i><font color="Green">E413</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> &amp; <font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font> &amp; <font color="Maroon">md</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">n4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">n4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">md</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">n4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/>

<b>assume </b><a NAME="E2:46_10"/><i><font color="Green">E414</font></i>: 
( <font color="Maroon">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<b>assume </b><a NAME="E3:46_10"/><i><font color="Green">E415</font></i>: 
( <font color="Maroon">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<a NAME="E4:46_10"/><i><font color="Green">E416</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E5:46_10"/><i><font color="Green">E417</font></i>: 
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="txt" href="scpqsort.html#E4"><i><font color="Green">Lemma48</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E6:46_10"/><b>then </b>
<font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E7:46_10"/><b>then </b><i><font color="Green">E418</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">md</font>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E8:46_10"/>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E9:46_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E10:46_10"/><b>then </b><i><font color="Green">E419</font></i>: 
<font color="Maroon">n4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E11:46_10"/><i><font color="Green">E420</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E12:46_10"/><b>then </b><i><font color="Green">E421</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E13:46_10"/><i><font color="Green">E422</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E14:46_10"/><i><font color="Green">E423</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, </i>;<br/>
<a NAME="E15:46_10"/><b>then </b><i><font color="Green">E424</font></i>: 
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i>, , <a class="ref" href="scmpds_6.html#T82">SCMPDS_6:82</a></i>;<br/>
<div><i><font color="Green">E425</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , , </i>
;<br/></div><b>end;</b></div>
<a NAME="E17:46_10"/><i><font color="Green">E426</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_2"/><i><font color="Green">E427</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><a NAME="E2:46_10_2"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_10_2"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_2"/><b>then </b><i><font color="Green">E428</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, , <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<a NAME="E19:46_10"/><b>then </b><i><font color="Green">E429</font></i>: 
<font color="Maroon">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_3"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> )
 ;<br/><b>hence </b><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div>
<a NAME="E21:46_10"/><b>then </b><i><font color="Green">E430</font></i>: 
<font color="Maroon">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E22:46_10"/><b>then </b><i><font color="Green">E431</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> 2 &amp; <font color="Maroon">md</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">n4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) )
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , </i>;<br/>
<b>hence </b><a NAME="E23:46_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E24:46_10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E25:46_10"/>
<font color="Maroon">md</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E26:46_10"/>
<font color="Maroon">n4</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_4"/><i><font color="Green">E432</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m1</font> )
 ;<br/><a NAME="E2:46_10_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_10_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="ref" href="scpqsort.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_4"/><b>then </b><i><font color="Green">E433</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , , , </i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, </i>
;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E28:46_10"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , , </i>;<br/>

<b>consider </b><font color="Maroon">m4</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E30:46_10"/><i><font color="Green">E434</font></i>: 
( <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m4</font> &amp; <font color="Maroon">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> &amp; <font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">m4</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> ) or ( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> ) )
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , , </i>;<br/>
<b>take </b>
<font color="Maroon">m4</font>
;<br/>

<b>thus </b><a NAME="E31:46_10"/>
( <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m4</font> &amp; <font color="Maroon">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> )
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E32:46_10"/>
<font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E33:46_10"/>
<font color="Maroon">m4</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_5"/>
( <font color="Maroon">md</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m4</font> )
 ;<br/><a NAME="E2:46_10_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:46_10_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:46_10_5"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_6"/>
( <font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n4</font> )
 ;<br/><a NAME="E2:46_10_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:46_10_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:46_10_6"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_10_7"/><i><font color="Green">E435</font></i>: 
( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> ) or ( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_10_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_10_7_1_1"/>
( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> ) or ( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1_1"><b>suppose </b></a><a NAME="E1:46_10_7_1_1_1"/>
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">md</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_10_7_1_1_1"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_10_7_1_1_2"><b>suppose </b></a><a NAME="E1:46_10_7_1_1_2"/>
( <font color="Maroon">n4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/><div class="add"><a NAME="E2:46_10_7_1_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">m4</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_10_7_1_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">md</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><a NAME="E4:46_10_7_1_1_2"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:46_10_7"/><b>then </b>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_10_7"/><b>then </b><i><font color="Green">E436</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, </i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E18:46"/><i><font color="Green">E437</font></i>: 
for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">m</font> &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">m</font> <a href="xcmplx_0.html#K6">-</a> 2 &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">mp</font> = <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/>
<b>assume </b><a NAME="E1:46_11"/><i><font color="Green">E438</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:46_11"/><b>then </b><i><font color="Green">E439</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:46_11"/><i><font color="Green">E440</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<a NAME="E4:46_11"/><b>then </b><i><font color="Green">E441</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E5:46_11"/><i><font color="Green">E442</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<a NAME="E6:46_11"/>
(  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/>
<a NAME="E7:46_11"/><b>then </b><i><font color="Green">E443</font></i>: 
(  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> &amp;  <a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_6.html#T83">SCMPDS_6:83</a></i>;<br/>
<b>set </b><font color="Maroon">li</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span>;<br/>
<div><i><font color="Green">E445</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_6.html#T88">SCMPDS_6:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:46_11"/><i><font color="Green">E446</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<a NAME="E10:46_11"/>
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/>
<a NAME="E11:46_11"/><b>then </b><i><font color="Green">E447</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E448</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_11_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_11_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><a NAME="E2:46_11_2"/><b>then </b><i><font color="Green">E449</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:46_11"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2

<br/>.= 
<font color="Maroon">m</font> <a href="xcmplx_0.html#K6">-</a> 2
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_11_4"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> )
 ;<br/><a NAME="E2:46_11_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_11_4"/><b>then </b><i><font color="Green">E450</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i><a class="ref" href="scpqsort.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:46_11_4"/><b>then </b><i><font color="Green">E451</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_11_4"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, </i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_11_5"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 ;<br/><a NAME="E2:46_11_5"/><b>then </b><i><font color="Green">E452</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_11_5"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_11_5"/><b>then </b><i><font color="Green">E453</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_11_5"/><b>then </b><i><font color="Green">E454</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:46_11_5"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, </i>
;<br/><br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">b1</font> =  <a href="scmpds_2.html#K3">DataLoc</a> 0,1;<br/>
<a NAME="E19:46"/><i><font color="Green">E456</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> 0,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green">E457</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">f2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">k1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">y1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">yn</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>set </b><font color="Maroon">mm</font> = <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/><b>set </b><font color="Maroon">md</font> = <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font>;<br/><b>set </b><font color="Maroon">n4</font> = <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font>;<br/><b>assume </b><a NAME="E1:46_12"/><i><font color="Green">E458</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> &amp; <font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">k2</font></span>)</span> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> ) or <font color="Maroon">y1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">yn</font> ) )
 ;<br/><b>set </b><font color="Maroon">mp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>;<br/><a NAME="E2:46_12"/><i><font color="Green">E459</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E3:46_12"/><i><font color="Green">E460</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/><a NAME="E4:46_12"/><i><font color="Green">E461</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_1_1"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> ) or <font color="Maroon">y1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">yn</font> )
 </span><b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1_1"><b>case </b></a><a NAME="E1:46_12_1_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_12_1_1_1"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_1_1_2"><b>case </b></a><a NAME="E1:46_12_1_1_2"/>
<font color="Maroon">y1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">yn</font>
 ;<br/><div class="add"><a NAME="E2:46_12_1_1_2"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:46_12"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>consider </b><font color="Maroon">f3</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E8:46_12"/><i><font color="Green">E462</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f3</font> holds <br/><font color="Maroon">f3</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">i</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/><a NAME="E9:46_12"/><i><font color="Green">E463</font></i>: 
<font color="Maroon">f3</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">p0</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/><b>consider </b><font color="Maroon">f4</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E11:46_12"/><i><font color="Green">E464</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f4</font> holds <br/><font color="Maroon">f4</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">i</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2">SCPISORT:2</a></i>;<br/><a NAME="E12:46_12"/><i><font color="Green">E465</font></i>: 
<font color="Maroon">f4</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_2_1"/>
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> or <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1_1"><b>suppose </b></a><a NAME="E1:46_12_2_1_1"/>
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_12_2_1_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_2_1_2"><b>suppose </b></a><a NAME="E1:46_12_2_1_2"/><i><font color="Green">E466</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:46_12_2_1_2"/><b>then </b><i><font color="Green">E467</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E3:46_12_2_1_2"/>
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E4:46_12_2_1_2"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> ) )
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, , , , , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_3"/>
<font color="Maroon">y1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">yn</font>
 ;<br/><a NAME="E2:46_12_3"/><b>then </b><i><font color="Green">E468</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 2
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/><br/><b>thus </b><a NAME="E4:46_12_3"/>
for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Olive">j</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_4"/><i><font color="Green">E469</font></i>: 
<font color="Maroon">y1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">yn</font>
 ;<br/><a NAME="E2:46_12_4"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_12_4"/><b>then </b><i><font color="Green">E470</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E4:46_12_4"/><i><font color="Green">E471</font></i>: 
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, , , , , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 3

;<br/><br/><b>consider </b><font color="Maroon">m4</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E7:46_12_4"/><i><font color="Green">E472</font></i>: 
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m4</font> &amp; <font color="Maroon">m4</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> &amp; <font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">m4</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m4</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">m4</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">m4</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st ( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">j</font></span>)</span> ) )
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , , , , , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_12_4_2"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">yn</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> ) )
 ;<br/><a NAME="E2:46_12_4_2"/><b>then </b>
( ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> ) )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_2"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><a NAME="E9:46_12_4"/><i><font color="Green">E473</font></i>: 
<font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p0</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y1</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>reconsider </b><font color="Maroon">ym</font> = <font color="Maroon">m4</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">p0</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E11:46_12_4"/><i><font color="Green">E474</font></i>: 
<font color="Maroon">m4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font>
 ;<br/><b>take </b><font color="Maroon">ym</font> = <font color="Maroon">ym</font>;<br/><b>thus </b><a NAME="E12:46_12_4"/>
( <font color="Maroon">y1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">ym</font> &amp; <font color="Maroon">ym</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">yn</font> )
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><a NAME="E13:46_12_4"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">k2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, , , , , , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>thus </b><a NAME="E14:46_12_4"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, </i>;<br/><b>thus </b><a NAME="E15:46_12_4"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, </i>;<br/><b>thus </b><a NAME="E16:46_12_4"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, , , , , , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_12_4_3"/>
( <font color="Maroon">y1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">ym</font> )
 ;<br/><a NAME="E2:46_12_4_3"/><b>then </b>
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font> )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_3"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_12_4_4"/>
( <font color="Maroon">ym</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">yn</font> )
 ;<br/><a NAME="E2:46_12_4_4"/><b>then </b>
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> )
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E3:46_12_4_4"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">ym</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:46_12_5"/><i><font color="Green">E475</font></i>: 
( <font color="Maroon">f1</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp; <font color="Maroon">f2</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_12_5_1"/>
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> or <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1_1"><b>suppose </b></a><a NAME="E1:46_12_5_1_1"/><i><font color="Green">E476</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_12_5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_12_5_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:46_12_5_1_1_1"/><b>then </b><i><font color="Green">E477</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E3:46"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
;<br/><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:46_12_5_1_1"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_12_5_1_2"><b>suppose </b></a><a NAME="E1:46_12_5_1_2"/><i><font color="Green">E478</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:46_12_5_1_2"/><b>then </b><i><font color="Green">E479</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E3:46_12_5_1_2"/>
( <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">yn</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E4:46_12_5_1_2"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, , , <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div>
<a NAME="E21:46"/><i><font color="Green">E480</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t3</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t4</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span>;<br/>
<a NAME="E1:46_13"/><i><font color="Green">E481</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/>
<div><i><font color="Green">E482</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_13_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 ;<br/><a NAME="E2:46_13_1"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:46_13_1"/><b>then </b>
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><br/></div><b>end;</b></div>
<i><font color="Green">E483</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a>, <a class="ref" href="scmp_gcd.html#T7">SCMP_GCD:7</a></i>
;<br/>
<i><font color="Green">E484</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<div><i><font color="Green">E485</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_13_4"/><i><font color="Green">E486</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 ;<br/><a NAME="E2:46_13_4"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:46_13_4"/><b>then </b><i><font color="Green">E487</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<a NAME="E6:46_13"/><i><font color="Green">E488</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E7:46_13"/><b>then </b><i><font color="Green">E489</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E490</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E9:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="scpqsort.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E10:46_13"/><b>then </b><i><font color="Green">E491</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<i><font color="Green">E492</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
1
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<i><font color="Green">E493</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<div><i><font color="Green">E494</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_13_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_13_8"/><i><font color="Green">E495</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/><a NAME="E2:46_13_8"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E3:46_13_8"/><b>then </b><i><font color="Green">E496</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font>
 <b>by </b><i>, , <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<i><font color="Green">E497</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>

;<br/>
<a NAME="E15:46_13"/><b>then </b><i><font color="Green">E498</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<a NAME="E17:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E18:46_13"/><b>then </b><i><font color="Green">E499</font></i>: 
 <a href="scmp_gcd.html#K3">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a>, <a class="ref" href="scmp_gcd.html#D3">SCMP_GCD:def 3</a></i>
<br/>.= 
1
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<a NAME="E20:46_13"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E21:46_13"/><b>then </b><i><font color="Green">E500</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_13_14"/><i><font color="Green">E501</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font> )
 ;<br/><a NAME="E2:46_13_14"/>
<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_13_14"/><b>then </b><i><font color="Green">E502</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font>
 <b>by </b><i>, , <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
;<br/></div>
<b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E22:46"/><i><font color="Green">E503</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a></i>;<br/>
<a NAME="E23:46"/><b>then </b><i><font color="Green">E504</font></i>: 
(  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font> &amp;  <a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font> )
 
<b>by </b><i><a class="txt" href="scpqsort.html#E3"><i><font color="Green">Lemma45</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, </i>;<br/>
<a NAME="E24:46"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>
<b>hence </b><a NAME="E25:46"/>
 <a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">s</font>
 ;<br/>

<b>consider </b><font color="Maroon">f</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E27:46"/><i><font color="Green">E505</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">s</font>,<font color="Maroon">p0</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3">SCPISORT:3</a></i>;<br/>
<b>consider </b><font color="Maroon">g</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E29:46"/><i><font color="Green">E506</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">g</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font></span>)</span>,<font color="Maroon">s</font>,<font color="Maroon">p0</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3">SCPISORT:3</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>take </b>
<font color="Maroon">g</font>
;<br/>

<b>thus </b><a NAME="E30:46"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">s</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">g</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scpqsort.html#K2" target="_self">QuickSort</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font></span>)</span>,<font color="Maroon">s</font>,<font color="Maroon">p0</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, </i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_14"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_14"/><i><font color="Green">E507</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 ;<br/><a NAME="E2:46_14"/><b>then </b><i><font color="Green">E508</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:46_14"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:46_14"/><b>then </b><i><font color="Green">E509</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:46_14"/><i><font color="Green">E510</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, , </i>
;<br/></div><b>end;</b></div>
<a NAME="E32:46"/><b>then </b><i><font color="Green">E511</font></i>: 
<font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_15"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:46_15"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> )
 ;<br/><b>hence </b><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpqsort.html#E10:46"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E34:46"/><b>then </b>
<font color="Maroon">g</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <font color="Maroon">Pt</font></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,4</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K3">SBP</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,2</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 2</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a>  <a href="scmpds_2.html#K6">:=</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K3">SBP</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<b>hence </b><a NAME="E35:46"/>
( <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">g</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">n</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E3"><i><font color="Green">Lemma45</font></i></a>, <a class="txt" href="scpqsort.html#E5:46"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scpqsort.html#E6:46"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scpqsort.html#E8:46"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scpqsort.html#E9:46"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scpqsort.html#E11:46"><i><font color="Green">E64</font></i></a>, , , </i>;<br/>


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