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<b>let </b><font color="Maroon" title="c30">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c31">f</font>, <font color="Maroon" title="c32">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/><b>let </b><font color="Maroon" title="c33">m</font>, <font color="Maroon" title="c34">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>





<b>set </b><font color="Maroon" title="c35">a</font> =  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ;<br/>
<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c34">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> &amp; <font color="Maroon" title="c33">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c30">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 )
 ;<br/>

<b>assume </b><a NAME="E2:37"/><i><font color="Green" title="E26">A2</font></i>: 
( <font color="Maroon" title="c31">f</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c30">s</font>,<font color="Maroon" title="c33">m</font> &amp; <font color="Maroon" title="c32">g</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c30">s</font>,<font color="Maroon" title="c33">m</font> )
 ;<br/>

<b>assume </b><a NAME="E3:37"/><i><font color="Green" title="E27">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c31">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c32">g</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c31">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c34">n</font> &amp; <font color="Maroon" title="c31">f</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<font color="Maroon" title="c34">n</font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ] <b>means </b>for <font color="Olive" title="b1">t</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> &amp; <font color="Maroon" title="c33">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Olive" title="b2">f1</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Olive" title="b1">t</font>,<font color="Maroon" title="c33">m</font> &amp; <font color="Olive" title="b3">f2</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive" title="b1">t</font>,<font color="Maroon" title="c33">m</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">f2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> $1 &amp; <font color="Olive" title="b2">f1</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,$1 holds <br/>( <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Olive" title="b3">f2</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,$1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; ( for <font color="Olive" title="b4">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> $1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f1</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> ) &amp; ( for <font color="Olive" title="b4">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">i</font> &amp; <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/> ex <font color="Olive" title="b5">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">j</font> &amp; <font color="Olive" title="b5">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">j</font> ) ) );<br/>
<a NAME="E4:37"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c36">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c37">f1</font>, <font color="Maroon" title="c38">f2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/>



<b>assume </b><a NAME="E1:37_1"/><i><font color="Green" title="E29">A5</font></i>: 
( <font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> &amp; <font color="Maroon" title="c33">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Maroon" title="c37">f1</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c36">t</font>,<font color="Maroon" title="c33">m</font> &amp; <font color="Maroon" title="c38">f2</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c36">t</font>,<font color="Maroon" title="c33">m</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c37">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c37">f1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c37">f1</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1, <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:37_1"/><b>then </b><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,6</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" title="SCMP_GCD:th.5">SCMP_GCD:5</a></i>;<br/>
<div><i><font color="Green" title="E31">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c39">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><a NAME="E1:37_1_1"/><i><font color="Green" title="E32">A8</font></i>: 
<font color="Maroon" title="c39">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><b>assume </b><a NAME="E2:37_1_1"/><i><font color="Green" title="E33">A9</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c39">i</font> &amp; <font color="Maroon" title="c39">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c37">f1</font> )
 ;<br/><b>hence </b><font color="Maroon" title="c37">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">i</font> = 
<font color="Maroon" title="c36">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c39">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="scpisort.html#E1:37_1_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c36">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c39">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E2:37_1"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="scmpds_8.html#T23" title="SCMPDS_8:th.23">SCMPDS_8:23</a></i>
<br/>.= 
<font color="Maroon" title="c38">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="scpisort.html#E1:37_1_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="txt" href="scpisort.html#E2:37_1_1"><i><font color="Green" title="E33">A9</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E4:37_1"/><b>then </b><i><font color="Green" title="E32">A10</font></i>: 
<font color="Maroon" title="c37">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f2</font>
 
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>
<b>thus </b><a NAME="E5:37_1"/>
<font color="Maroon" title="c37">f1</font>,<font color="Maroon" title="c38">f2</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="scpisort.html#E3:37_1"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>

<b>thus </b><a NAME="E6:37_1"/>
<font color="Maroon" title="c38">f2</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="scpisort.html#T1" target="_self" title="SCPISORT:th.1">Th1</a></i>;<br/>

<b>thus </b><a NAME="E7:37_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c37">f1</font> holds <br/><font color="Maroon" title="c37">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_1"><i><font color="Green" title="E31">A7</font></i></a></i>;<br/>

<b>thus </b><a NAME="E8:37_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/> ex <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c38">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> )
 <b>by </b><i><a class="txt" href="scpisort.html#E4:37_1"><i><font color="Green" title="E32">A10</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E29">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c36">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2"/><i><font color="Green" title="E30">A12</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c36">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c37">t</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c38">f1</font>, <font color="Maroon" title="c39">f2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1"/><i><font color="Green" title="E31">A13</font></i>: 
( <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> &amp; <font color="Maroon" title="c33">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Maroon" title="c38">f1</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c37">t</font>,<font color="Maroon" title="c33">m</font> &amp; <font color="Maroon" title="c39">f2</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font>,<font color="Maroon" title="c33">m</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c39">f2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c38">f1</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 ;<br/><b>set </b><font color="Maroon" title="c40">Bt</font> =  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font>;<br/><b>set </b><font color="Maroon" title="c41">x</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon" title="c42">y</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/><i><font color="Green" title="E32">A14</font></i>:  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> = 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <font color="Maroon" title="c33">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" title="SCMP_GCD:th.5">SCMP_GCD:5</a></i>
;<br/><a NAME="E3:37_2_1"/><i><font color="Green" title="E33">A15</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" title="SCMP_GCD:th.5">SCMP_GCD:5</a></i>;<br/><a NAME="E4:37_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a></i>;<br/><a NAME="E5:37_2_1"/><b>then </b><i><font color="Green" title="E34">A16</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E6:37_2_1"/><i><font color="Green" title="E35">A17</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">i</font></span>)</span> ) &amp; ( <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 ) ) &amp; ( <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) ) )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E24"><i><font color="Green" title="E16">Lm7</font></i></a>, <a class="txt" href="scpisort.html#E23"><i><font color="Green" title="E15">Lm7A</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2"/>
( <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> or <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1"/><i><font color="Green" title="E36">A18</font></i>: 
<font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ;<br/><div class="add"><b>consider </b><font color="Maroon" title="c43">h</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E3:37_2_1_2_1"/><i><font color="Green" title="E37">A19</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c43">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c43">h</font> holds <br/><font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="ref" href="scpisort.html#T2" target="_self" title="SCPISORT:th.2">Th2</a></i>;<br/><a NAME="E4:37_2_1_2_1"/><i><font color="Green" title="E38">A20</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">m</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a></i>;<br/><a NAME="E5:37_2_1_2_1"/><i><font color="Green" title="E39">A21</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font>,<font color="Maroon" title="c33">m</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c39">f2</font> )
 ;<br/><b>hence </b><font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E33"><i><font color="Green" title="E23">Lm14</font></i></a></i>
;<br/><br/></div><b>end;</b></div><a NAME="E7:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E40">A22</font></i>: 
<font color="Maroon" title="c39">f2</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span>,<font color="Maroon" title="c33">m</font>
 <b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><a NAME="E8:37_2_1_2_1"/>
<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c36">k</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E9:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E41">A23</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c43">h</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c36">k</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><div><i><font color="Green" title="E42">A24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_2"/><i><font color="Green" title="E43">A25</font></i>: 
( <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> )
 ;<br/><a NAME="E2:37_2_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E3:37_2_1_2_1_2"/><b>then </b><i><font color="Green" title="E44">A26</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7
 <b>by </b><i><a class="txt" href="scpisort.html#E5:37_2_1"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E4:37_2_1_2_1_2"/><i><font color="Green" title="E45">A27</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_2"><i><font color="Green" title="E43">A25</font></i></a></i>;<br/><a NAME="E5:37_2_1_2_1_2"/><i><font color="Green" title="E46">A28</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_2"><i><font color="Green" title="E43">A25</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_2"><i><font color="Green" title="E43">A25</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c44">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1_2"><i><font color="Green" title="E44">A26</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1_2"><i><font color="Green" title="E45">A27</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="txt" href="scpisort.html#E24"><i><font color="Green" title="E16">Lm7</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_2"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c44">i</font>, <font color="Maroon" title="c45">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_3"/><i><font color="Green" title="E43">A29</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c45">j</font> &amp; <font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> )
 ;<br/><a NAME="E2:37_2_1_2_1_3"/><i><font color="Green" title="E44">A30</font></i>: 
<font color="Maroon" title="c36">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E3:37_2_1_2_1_3"/>
<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E4:37_2_1_2_1_3"/><b>then </b><i><font color="Green" title="E45">A31</font></i>: 
<font color="Maroon" title="c36">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E2:37_2_1_2_1_3"><i><font color="Green" title="E44">A30</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:37_2_1_2_1_3"/><i><font color="Green" title="E46">A32</font></i>: 
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_1_3"><i><font color="Green" title="E44">A30</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:37_2_1_2_1_3"/><i><font color="Green" title="E47">A33</font></i>: 
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1_3"><i><font color="Green" title="E45">A31</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E7:37_2_1_2_1_3"/><i><font color="Green" title="E48">A34</font></i>: 
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E8:37_2_1_2_1_3"/>
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E9:37_2_1_2_1_3"/><b>then </b><i><font color="Green" title="E49">A35</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_1_3"><i><font color="Green" title="E44">A30</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1_3"><i><font color="Green" title="E45">A31</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1_3"><i><font color="Green" title="E48">A34</font></i></a></i>;<br/><a NAME="E10:37_2_1_2_1_3"/>
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1_3"><i><font color="Green" title="E48">A34</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E11:37_2_1_2_1_3"/><b>then </b>
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_3"><i><font color="Green" title="E46">A32</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_1_3"><i><font color="Green" title="E47">A33</font></i></a></i>;<br/><b>hence </b><a NAME="E12:37_2_1_2_1_3"/>
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_3"><i><font color="Green" title="E43">A29</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_3"><i><font color="Green" title="E46">A32</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1_3"><i><font color="Green" title="E49">A35</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/></div><b>end;</b></div><a NAME="E12:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E43">A36</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<font color="Maroon" title="c36">k</font>
 <b>by </b><i><a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/><a NAME="E13:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E44">A37</font></i>: 
( <font color="Maroon" title="c43">h</font>,<font color="Maroon" title="c39">f2</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon" title="c39">f2</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c43">h</font> holds <br/><font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/> ex <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> ) ) )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a></i>;<br/><a NAME="E14:37_2_1_2_1"/><i><font color="Green" title="E45">A38</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E15:37_2_1_2_1"/><i><font color="Green" title="E46">A39</font></i>: 
<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E16:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E47">A40</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="txt" href="scpisort.html#E14:37_2_1_2_1"><i><font color="Green" title="E45">A38</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E17:37_2_1_2_1"/><i><font color="Green" title="E48">A41</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E18:37_2_1_2_1"/><i><font color="Green" title="E49">A42</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E14:37_2_1_2_1"><i><font color="Green" title="E45">A38</font></i></a></i>;<br/><a NAME="E19:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E50">A43</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E16:37_2_1_2_1"><i><font color="Green" title="E47">A40</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><a NAME="E20:37_2_1_2_1"/><i><font color="Green" title="E51">A44</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E16:37_2_1_2_1"><i><font color="Green" title="E47">A40</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a></i>;<br/><a NAME="E21:37_2_1_2_1"/><b>then </b><i><font color="Green" title="E52">A45</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E14:37_2_1_2_1"><i><font color="Green" title="E45">A38</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><a NAME="E22:37_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c38">f1</font>,<font color="Maroon" title="c43">h</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E14:37_2_1_2_1"><i><font color="Green" title="E45">A38</font></i></a>, <a class="txt" href="scpisort.html#E16:37_2_1_2_1"><i><font color="Green" title="E47">A40</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="txt" href="scpisort.html#E19:37_2_1_2_1"><i><font color="Green" title="E50">A43</font></i></a>, <a class="ref" href="scpisort.html#T4" target="_self" title="SCPISORT:th.4">Th4</a></i>;<br/><b>hence </b><a NAME="E23:37_2_1_2_1"/>
<font color="Maroon" title="c38">f1</font>,<font color="Maroon" title="c39">f2</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E13:37_2_1_2_1"><i><font color="Green" title="E44">A37</font></i></a>, <a class="ref" href="rfinseq.html#T2" title="RFINSEQ:th.2">RFINSEQ:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c44">i</font>, <font color="Maroon" title="c45">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_4"/><i><font color="Green" title="E53">A46</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c45">j</font> &amp; <font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_1_4_1"/>
( <font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c45">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_4"><i><font color="Green" title="E53">A46</font></i></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_1"/>
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_2_1_2_1_4_1_1"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E13:37_2_1_2_1"><i><font color="Green" title="E44">A37</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_4"><i><font color="Green" title="E53">A46</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_2"/><i><font color="Green" title="E54">A47</font></i>: 
<font color="Maroon" title="c45">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_1_4_1_2_1_1"/>
( <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c45">j</font> or <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c45">j</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_2_1_1_1"/>
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c45">j</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_2_1_2_1_4_1_2_1_1_1"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_2_1_1_2"/>
<font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c45">j</font>
 ;<br/><div class="add"><a NAME="E2:37_2_1_2_1_4_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_4"><i><font color="Green" title="E53">A46</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:37_2_1_2_1_4_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_4_1_2"><i><font color="Green" title="E54">A47</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c46">mm</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E5:37_2_1_2_1_4_1_2_1_1_2"/><i><font color="Green" title="E55">A48</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c46">mm</font> &amp; <font color="Maroon" title="c46">mm</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">mm</font> )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E12:37_2_1_2_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_4"><i><font color="Green" title="E53">A46</font></i></a></i>;<br/><a NAME="E6:37_2_1_2_1_4_1_2_1_1_2"/><i><font color="Green" title="E56">A49</font></i>: 
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E12:37_2_1_2_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_4_1_2"><i><font color="Green" title="E54">A47</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_1_4_1_2_1_1_2_1_1"/>
( <font color="Maroon" title="c46">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c46">mm</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c46">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_2_1_2_1_4_1_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E20:37_2_1_2_1"><i><font color="Green" title="E51">A44</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E55">A48</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E56">A49</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_4_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/><i><font color="Green" title="E57">A50</font></i>: 
<font color="Maroon" title="c46">mm</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><a NAME="E2:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon" title="c46">mm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E55">A48</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E3:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c46">mm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c43">h</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E4:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E58">A51</font></i>: 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">mm</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E55">A48</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_4_1_2_1_1_2_1_1_2"><i><font color="Green" title="E57">A50</font></i></a></i>;<br/><a NAME="E5:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E14:37_2_1_2_1"><i><font color="Green" title="E45">A38</font></i></a>, <a class="txt" href="scpisort.html#E20:37_2_1_2_1"><i><font color="Green" title="E51">A44</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E56">A49</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E6:37_2_1_2_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_4_1_2_1_1_2"><i><font color="Green" title="E55">A48</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1_4_1_2_1_1_2_1_1_2"><i><font color="Green" title="E58">A51</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E25:37_2_1_2_1"/>
<font color="Maroon" title="c39">f2</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_5"/><i><font color="Green" title="E53">A52</font></i>: 
( <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> )
 ;<br/><a NAME="E2:37_2_1_2_1_5"/><i><font color="Green" title="E54">A53</font></i>: 
<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E3:37_2_1_2_1_5"/><b>then </b><i><font color="Green" title="E55">A54</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_5"><i><font color="Green" title="E53">A52</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E4:37_2_1_2_1_5"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:37_2_1_2_1_5"/><b>then </b><i><font color="Green" title="E56">A55</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_1_5"><i><font color="Green" title="E55">A54</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>thus </b><font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> = 
<font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E12:37_2_1_2_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_5"><i><font color="Green" title="E53">A52</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1_5"><i><font color="Green" title="E55">A54</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_5"><i><font color="Green" title="E53">A52</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_1_5"><i><font color="Green" title="E54">A53</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_5"><i><font color="Green" title="E56">A55</font></i></a></i>
;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c44">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_1_6"/><i><font color="Green" title="E53">A56</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">i</font> &amp; <font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_1_6_1"/>
( <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_6_1_1"/><i><font color="Green" title="E54">A57</font></i>: 
<font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c45">j</font> = <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><b>thus </b><a NAME="E2:37_2_1_2_1_6_1_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>thus </b><a NAME="E3:37_2_1_2_1_6_1_1"/>
<font color="Maroon" title="c45">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>thus </b><a NAME="E4:37_2_1_2_1_6_1_1"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E12:37_2_1_2_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="txt" href="scpisort.html#E21:37_2_1_2_1"><i><font color="Green" title="E52">A45</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_6_1_1"><i><font color="Green" title="E54">A57</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_6_1_2"/>
<font color="Maroon" title="c44">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><a NAME="E2:37_2_1_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_6"><i><font color="Green" title="E53">A56</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:37_2_1_2_1_6_1_2"/><b>then </b>
<font color="Maroon" title="c44">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>then consider </b><font color="Maroon" title="c45">mm</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E5:37_2_1_2_1_6_1_2"/><i><font color="Green" title="E54">A58</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c45">mm</font> &amp; <font color="Maroon" title="c45">mm</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c43">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c45">mm</font> )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1"><i><font color="Green" title="E36">A18</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1"><i><font color="Green" title="E37">A19</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_1"><i><font color="Green" title="E38">A20</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1"><i><font color="Green" title="E39">A21</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_1"><i><font color="Green" title="E40">A22</font></i></a>, <a class="txt" href="scpisort.html#E9:37_2_1_2_1"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scpisort.html#E12:37_2_1_2_1"><i><font color="Green" title="E43">A36</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_6"><i><font color="Green" title="E53">A56</font></i></a></i>;<br/><div><b>hereby </b>
<div class="add"><a NAME="E1:37_2_1_2_1_6_1_2_1"/><i><font color="Green" title="E55">A59</font></i>: 
<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_1_6_1_2_1_1"/>
( <font color="Maroon" title="c45">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c45">mm</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_6_1_2_1_1_1"/><i><font color="Green" title="E56">A60</font></i>: 
<font color="Maroon" title="c45">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c46">j</font> = <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2;<br/><b>thus </b><a NAME="E2:37_2_1_2_1_6_1_2_1_1_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c46">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_1_6_1_2_1"><i><font color="Green" title="E55">A59</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>thus </b><a NAME="E3:37_2_1_2_1_6_1_2_1_1_1"/>
<font color="Maroon" title="c46">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><b>thus </b><a NAME="E4:37_2_1_2_1_6_1_2_1_1_1"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E16:37_2_1_2_1"><i><font color="Green" title="E47">A40</font></i></a>, <a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="txt" href="scpisort.html#E18:37_2_1_2_1"><i><font color="Green" title="E49">A42</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_6_1_2"><i><font color="Green" title="E54">A58</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_6_1_2_1_1_1"><i><font color="Green" title="E56">A60</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_1_6_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_1_6_1_2_1_1_2"/><i><font color="Green" title="E56">A61</font></i>: 
<font color="Maroon" title="c45">mm</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><a NAME="E2:37_2_1_2_1_6_1_2_1_1_2"/>
<font color="Maroon" title="c45">mm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_6_1_2"><i><font color="Green" title="E54">A58</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E3:37_2_1_2_1_6_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E57">A62</font></i>: 
<font color="Maroon" title="c45">mm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E17:37_2_1_2_1"><i><font color="Green" title="E48">A41</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>take </b><font color="Maroon" title="c46">mm</font> = <font color="Maroon" title="c45">mm</font>;<br/><b>thus </b><a NAME="E4:37_2_1_2_1_6_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c46">mm</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E5:37_2_1_2_1_6_1_2"><i><font color="Green" title="E54">A58</font></i></a></i>;<br/><b>thus </b><a NAME="E5:37_2_1_2_1_6_1_2_1_1_2"/>
<font color="Maroon" title="c46">mm</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_6_1_2"><i><font color="Green" title="E54">A58</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>thus </b><a NAME="E6:37_2_1_2_1_6_1_2_1_1_2"/>
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c46">mm</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E10:37_2_1_2_1"><i><font color="Green" title="E42">A24</font></i></a>, <a class="txt" href="scpisort.html#E15:37_2_1_2_1"><i><font color="Green" title="E46">A39</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_1_6_1_2"><i><font color="Green" title="E54">A58</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_1_6_1_2_1_1_2"><i><font color="Green" title="E56">A61</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1_2_1_6_1_2_1_1_2"><i><font color="Green" title="E57">A62</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_2"/><i><font color="Green" title="E36">A63</font></i>: 
<font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ;<br/><div class="add"><div><i><font color="Green" title="E37">A64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c43">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><a NAME="E1:37_2_1_2_2_1"/><i><font color="Green" title="E38">A65</font></i>: 
<font color="Maroon" title="c43">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><b>assume </b><a NAME="E2:37_2_1_2_2_1"/><i><font color="Green" title="E39">A66</font></i>: 
( <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> )
 ;<br/><a NAME="E3:37_2_1_2_2_1"/><b>then </b>
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E4:37_2_1_2_2_1"/><b>then </b><i><font color="Green" title="E40">A67</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 7
 <b>by </b><i><a class="txt" href="scpisort.html#E5:37_2_1"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:37_2_1_2_2_1"/><i><font color="Green" title="E41">A68</font></i>: 
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_1"><i><font color="Green" title="E38">A65</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2_1"><i><font color="Green" title="E39">A66</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><a NAME="E6:37_2_1_2_2_1"/><i><font color="Green" title="E42">A69</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> </span>)</span>,6</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2"><i><font color="Green" title="E36">A63</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" title="SCMP_GCD:th.5">SCMP_GCD:5</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_2_1_1"/>
( <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 or <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> or ( <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_1_1_1"/><i><font color="Green" title="E43">A70</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2"><i><font color="Green" title="E36">A63</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_2_1"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_2_1"><i><font color="Green" title="E42">A69</font></i></a>, <a class="ref" href="scmpds_8.html#T23" title="SCMPDS_8:th.23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E33"><i><font color="Green" title="E23">Lm14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2_1"><i><font color="Green" title="E39">A66</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_1_1_1"><i><font color="Green" title="E43">A70</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_1_1_2"/><i><font color="Green" title="E43">A71</font></i>: 
<font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1"><i><font color="Green" title="E35">A17</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2"><i><font color="Green" title="E36">A63</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_2_1"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_2_1"><i><font color="Green" title="E42">A69</font></i></a>, <a class="ref" href="scmpds_8.html#T23" title="SCMPDS_8:th.23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E33"><i><font color="Green" title="E23">Lm14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2_1"><i><font color="Green" title="E39">A66</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_1_1_2"><i><font color="Green" title="E43">A71</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_1_1_3"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_1_1_3"/>
( <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_2_1"><i><font color="Green" title="E40">A67</font></i></a>, <a class="txt" href="scpisort.html#E5:37_2_1_2_2_1"><i><font color="Green" title="E41">A68</font></i></a>, <a class="txt" href="scpisort.html#E24"><i><font color="Green" title="E16">Lm7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">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" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E6:37_2_1_2_2_1"><i><font color="Green" title="E42">A69</font></i></a>, <a class="ref" href="scmpds_8.html#T23" title="SCMPDS_8:th.23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3" title="SCMPDS_8:func.3">while&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3" title="SCMPDS_6:func.3">if&gt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5,<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#K2" title="SCMP_GCD:func.2">GBP</a> ,5 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,6 <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c37">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c33">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c43">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E33"><i><font color="Green" title="E23">Lm14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_1"><i><font color="Green" title="E38">A65</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2_1"><i><font color="Green" title="E39">A66</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:37_2_1_2_2"/><b>then </b><i><font color="Green" title="E38">A72</font></i>: 
<font color="Maroon" title="c38">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c39">f2</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/><b>thus </b><a NAME="E4:37_2_1_2_2"/>
<font color="Maroon" title="c38">f1</font>,<font color="Maroon" title="c39">f2</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2"><i><font color="Green" title="E37">A64</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_2_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c43">i</font>, <font color="Maroon" title="c44">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:37_2_1_2_2_2"/><i><font color="Green" title="E39">A73</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c43">i</font> &amp; <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c44">j</font> &amp; <font color="Maroon" title="c44">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_2_2_1"/>
( <font color="Maroon" title="c44">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c44">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_2_2"><i><font color="Green" title="E39">A73</font></i></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_2_1_1"/>
<font color="Maroon" title="c44">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_2_1_2_2_2_1_1"/>
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_2"><i><font color="Green" title="E39">A73</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_2_1_2"/><i><font color="Green" title="E40">A74</font></i>: 
<font color="Maroon" title="c44">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1_2_2_2_1_2_1_1"/>
( <font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c44">j</font> or <font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c44">j</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_2_1_2_1_1_1"/>
<font color="Maroon" title="c43">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c44">j</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:37_2_1_2_2_2_1_2_1_1_1"/>
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">j</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2_2_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2_2_2_1_2_1_1_2"/>
<font color="Maroon" title="c43">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c44">j</font>
 ;<br/><div class="add"><a NAME="E2:37_2_1_2_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c44">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_2_2"><i><font color="Green" title="E39">A73</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:37_2_1_2_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_2_2_1_2"><i><font color="Green" title="E40">A74</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:37_2_1_2_2_2_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E41">A75</font></i>: 
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_2"><i><font color="Green" title="E39">A73</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/><a NAME="E5:37_2_1_2_2_2_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E6:37_2_1_2_2_2_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E42">A76</font></i>: 
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><a NAME="E7:37_2_1_2_2_2_1_2_1_1_2"/><i><font color="Green" title="E43">A77</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E8:37_2_1_2_2_2_1_2_1_1_2"/>
<font color="Maroon" title="c44">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_2_1_2"><i><font color="Green" title="E40">A74</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E9:37_2_1_2_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c37">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 4</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E3:37_2_1"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scpisort.html#E1:37_2_1_2_2_2_1_2"><i><font color="Green" title="E40">A74</font></i></a>, <a class="txt" href="scpisort.html#E7:37_2_1_2_2_2_1_2_1_1_2"><i><font color="Green" title="E43">A77</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self" title="SCPISORT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E10:37_2_1_2_2_2_1_2_1_1_2"/>
<font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c43">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c44">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1_2_2"><i><font color="Green" title="E36">A63</font></i></a>, <a class="txt" href="scpisort.html#E4:37_2_1_2_2_2_1_2_1_1_2"><i><font color="Green" title="E41">A75</font></i></a>, <a class="txt" href="scpisort.html#E6:37_2_1_2_2_2_1_2_1_1_2"><i><font color="Green" title="E42">A76</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:37_2_1_2_2"/>
<font color="Maroon" title="c39">f2</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_2"><i><font color="Green" title="E38">A72</font></i></a>, <a class="ref" href="graph_2.html#D13" title="GRAPH_2:def.13">GRAPH_2:def 13</a></i>;<br/><b>thus </b><a NAME="E7:37_2_1_2_2"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c38">f1</font> holds <br/><font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37_2_1"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="scpisort.html#E2:37_2_1_2_2"><i><font color="Green" title="E37">A64</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/><b>thus </b><a NAME="E8:37_2_1_2_2"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/> ex <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c39">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> )
 <b>by </b><i><a class="txt" href="scpisort.html#E3:37_2_1_2_2"><i><font color="Green" title="E38">A72</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:37_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c36">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E6:37"/>
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="scpisort.html#E4:37"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="scpisort.html#E5:37"><i><font color="Green" title="E29">A11</font></i></a>);<br/></i>
<b>hence </b><a NAME="E7:37"/>
( <font color="Maroon" title="c31">f</font>,<font color="Maroon" title="c32">g</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon" title="c32">g</font> <a href="graph_2.html#R3" title="GRAPH_2:pred.3">is_non_decreasing_on</a> 1,<font color="Maroon" title="c34">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c34">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c31">f</font> holds <br/><font color="Maroon" title="c31">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c34">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/> ex <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c34">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c32">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> ) ) )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:37"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="scpisort.html#E2:37"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="scpisort.html#E3:37"><i><font color="Green" title="E27">A3</font></i></a></i>;<br/>


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