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<span class="kw">let </span><font color="Maroon" title="c27">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st <font color="Olive" title="b1">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="Olive" title="b1">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> 1</span>)</span> <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="Olive" title="b1">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> 2</span>)</span> <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="Olive" title="b1">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> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 2</span>)</span></span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Olive" title="b1">s</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> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Olive" title="b1">s</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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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> 2</span>)</span></span>)</span> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c27">P</font> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c27">P</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c28">a</font> =  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c29">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c29">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="c29">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> 1</span>)</span> <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="c29">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> 2</span>)</span> <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="c29">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> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> ) )</span><br/>

<a NAME="E1:43"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3) <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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E29">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c30">t</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Q</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st <font color="Maroon" title="c30">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> <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="c30">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> 2</span>)</span> <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="c30">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="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <font color="Maroon" title="c30">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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> holds <br/>( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c30">t</font>,<font color="Olive" title="b1">Q</font> &amp; <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Olive" title="b1">Q</font> &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c31">Q</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c30">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> <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="c30">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> 2</span>)</span> <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="c30">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="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <font color="Maroon" title="c30">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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:43_1"/>
<font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:43_1"/>
<font color="Maroon" title="c30">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> 2</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E3:43_1"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c30">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> 
 <span class="kw">and </span><br/><a NAME="E4:43_1"/><span class="lab"><font color="Green" title="E31">A4</font></span>: 
<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:43_1"/>
<font color="Maroon" title="c30">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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E6:43_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="scpinvar.html#E34"><span class="lab"><font color="Green" title="E26">Lm14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E7:43_1"/>
<span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T20" title="SCMPDS_6:th.20">SCMPDS_6:20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font> &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E8:43_1"/>
<span class="p1">(<span class="default"><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>,3,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</span>)</span></span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p1">(<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>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c30">t</font>,<font color="Maroon" title="c31">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T21" title="SCMPDS_6:th.21">SCMPDS_6:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> ) ) &amp; ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span><br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:43_1_1"/>
<font color="Maroon" title="c30">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> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c30">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> 2</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> )</span><br/><a NAME="E2:43_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c30">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> 3</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="xreal_1.html#T50" title="XREAL_1:th.50">XREAL_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_1_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">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> 2</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="scpinvar.html#E34"><span class="lab"><font color="Green" title="E26">Lm14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span></span>
<div class="add"><span class="kw">assume </span><a NAME="E1:43_1_2"/>
<font color="Maroon" title="c30">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> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">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> 2</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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> )</span><br/><a NAME="E2:43_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c30">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> 3</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="xreal_1.html#T47" title="XREAL_1:th.47">XREAL_1:47</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_1_2"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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="c30">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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="scpinvar.html#E34"><span class="lab"><font color="Green" title="E26">Lm14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div><span class="kw">thus </span><a NAME="E11:43_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><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>,3,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p4">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,3)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<font color="Maroon" title="c31">Q</font>,<font color="Maroon" title="c30">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> 2</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="scpinvar.html#E34"><span class="lab"><font color="Green" title="E26">Lm14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:43"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
( <font color="Maroon" title="c29">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="c29">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> 1</span>)</span> <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="c29">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> 2</span>)</span> <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="c29">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> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> )</span><br/>

<span class="kw">hence </span><a NAME="E4:43"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><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>,3,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</a> <span class="p1">(<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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p5">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c27">P</font>,<font color="Maroon" title="c29">s</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> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c29">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> 2</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="scpinvar.html#T17" target="_self" title="SCPINVAR:th.17">Th21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> )</span><br/>

<span class="kw">thus </span><a NAME="E5:43"/>
(  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> &amp;  <a href="scpinvar.html#K4" title="SCPINVAR:func.4">while&lt;&gt;0</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>,3,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,1,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="compos_1.html#K14" title="COMPOS_1:func.14">Load</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>,2,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,1)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p3">(<span class="default">(<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3) <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>,1)</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_2.html#K14" title="SCMPDS_2:func.14">SubFrom</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c29">s</font>,<font color="Maroon" title="c27">P</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="scpinvar.html#E31"><span class="lab"><font color="Green" title="E24">Lm12</font></span></a>, <a class="ref" href="scpinvar.html#T16" target="_self" title="SCPINVAR:th.16">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
