<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c11">a</font> =  <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ;<br/>
<b>let </b><font color="Maroon" title="c12">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c13">n</font>, <font color="Maroon" title="c14">p0</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c15">f</font> be    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c14">p0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 &amp; <font color="Maroon" title="c15">f</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c12">s</font>,<font color="Maroon" title="c14">p0</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">n</font> &amp; <font color="Maroon" title="c12">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="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c12">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> 0 &amp; <font color="Maroon" title="c12">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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c13">n</font> &amp; <font color="Maroon" title="c12">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> <font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c16">t</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>given </b><font color="Maroon" title="c17">g</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> <b> such that </b><a NAME="E1:9_1"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c17">g</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c12">s</font>,<font color="Maroon" title="c14">p0</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">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#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">n</font> &amp; <font color="Maroon" title="c16">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#R1" title="HIDDEN:pred.1">=</a>  <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">Sum</a> <font color="Maroon" title="c17">g</font> &amp; <font color="Maroon" title="c16">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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span> )
 ;<br/><b>assume </b><a NAME="E2:9_1"/><i><font color="Green" title="E11">A3</font></i>: 
( <font color="Maroon" title="c16">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> 0 &amp; <font color="Maroon" title="c16">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#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 )
 ;<br/><b>assume </b><a NAME="E3:9_1"/><i><font color="Green" title="E12">A4</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c14">p0</font> holds <br/><font color="Maroon" title="c16">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">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> <font color="Olive" title="b1">i</font></span>)</span>
 ;<br/><b>thus </b><a NAME="E4:9_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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> 0
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="scpinvar.html#E11"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/><b>thus </b><a NAME="E5:9_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c16">t</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c16">t</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34" title="SCMPDS_6:th.34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35" title="SCMPDS_6:th.35">SCMPDS_6:35</a></i>;<br/><b>thus </b><a NAME="E6:9_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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="c16">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#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="scpinvar.html#E11"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/><b>thus </b><a NAME="E7:9_1"/>
 ex <font color="Olive" title="b1">g</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  st <br/>( <font color="Olive" title="b1">g</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c12">s</font>,<font color="Maroon" title="c14">p0</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">g</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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>  <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">Sum</a> <font color="Olive" title="b1">g</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c18">h</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> <b> such that </b><br/><a NAME="E2:9_1_1"/><i><font color="Green" title="E13">A5</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c18">h</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c12">s</font>,<font color="Maroon" title="c14">p0</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3" title="SCPISORT:th.3">SCPISORT:3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c18">h</font>
;<br/>

<b>thus </b><a NAME="E3:9_1_1"/>
<font color="Maroon" title="c18">h</font> <a href="scpisort.html#R1" title="SCPISORT:pred.1">is_FinSequence_on</a> <font color="Maroon" title="c12">s</font>,<font color="Maroon" title="c14">p0</font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a></i>;<br/>

<b>thus </b><a NAME="E4:9_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c13">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a></i>;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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> 3</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="scpinvar.html#E11"><i><font color="Green" title="E6">Lm2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a></i>
;<br/>

<b>set </b><font color="Maroon" title="c19">m</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c20">q</font> = <font color="Maroon" title="c18">h</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a>  <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<div><i><font color="Green" title="E14">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:9_1_1_2"/><i><font color="Green" title="E15">A7</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">i</font> &amp; <font color="Maroon" title="c21">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_1_1_2_1"/>
( <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> or <font color="Maroon" title="c21">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:9_1_1_2_1_1"/>
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_1_1_2_1_1"/>
<font color="Maroon" title="c18">h</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Maroon" title="c21">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">g</font> <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">q</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="finseq_1.html#T59" title="FINSEQ_1:th.59">FINSEQ_1:59</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:9_1_1_2_1_2"/>
<font color="Maroon" title="c21">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font>
 ;<br/><div class="add"><a NAME="E2:9_1_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c21">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1_1_2"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E3:9_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c21">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font>
 <b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/><a NAME="E4:9_1_1_2_1_2"/><b>then </b>
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1_1_2"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:9_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E17">A9</font></i>: 
<font color="Maroon" title="c21">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">g</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>thus </b><font color="Maroon" title="c18">h</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Maroon" title="c21">i</font> = 
<font color="Maroon" title="c12">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> <span class="p2">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c21">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="scpinvar.html#E1:9_1_1_2"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="scpisort.html#D1" title="SCPISORT:def.1">SCPISORT:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c17">g</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E1:9_1_1_2"><i><font color="Green" title="E15">A7</font></i></a>, <a class="txt" href="scpinvar.html#E3:9_1_1_2_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="scpisort.html#D1" title="SCPISORT:def.1">SCPISORT:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">g</font> <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">q</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <font color="Maroon" title="c21">i</font>
<b>by </b><i><a class="txt" href="scpinvar.html#E5:9_1_1_2_1_2"><i><font color="Green" title="E17">A9</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E8:9_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">g</font> <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">q</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font>
 
<b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="finseq_2.html#T19" title="FINSEQ_2:th.19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E9:9_1_1"/><b>then </b><i><font color="Green" title="E15">A10</font></i>: 
<font color="Maroon" title="c17">g</font> <a href="wsierp_1.html#K4" title="WSIERP_1:func.4">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c20">q</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">h</font>
 
<b>by </b><i><a class="txt" href="scpinvar.html#E7:9_1_1"><i><font color="Green" title="E14">A6</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>
<a NAME="E10:9_1_1"/><i><font color="Green" title="E16">A11</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E11:9_1_1"/><b>then </b><i><font color="Green" title="E17">A12</font></i>: 
<font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E12:9_1_1"/>
<font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c14">p0</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E13:9_1_1"/><b>then </b><i><font color="Green" title="E18">A13</font></i>: 
<font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c14">p0</font>
 
<b>by </b><i><a class="txt" href="scpinvar.html#E11:9_1_1"><i><font color="Green" title="E17">A12</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<font color="Maroon" title="c18">h</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span> = 
<font color="Maroon" title="c12">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> <span class="p2">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="scpinvar.html#E10:9_1_1"><i><font color="Green" title="E16">A11</font></i></a>, <a class="ref" href="scpisort.html#D1" title="SCPISORT:def.1">SCPISORT:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c16">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c14">p0</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E3:9_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1_1"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="scpinvar.html#E13:9_1_1"><i><font color="Green" title="E18">A13</font></i></a></i>
;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">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> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">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#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">h</font> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="scpinvar.html#E11"><i><font color="Green" title="E6">Lm2</font></i></a></i>
<br/>.= 
 <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">Sum</a> <font color="Maroon" title="c18">h</font>
<b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E9:9_1_1"><i><font color="Green" title="E15">A10</font></i></a>, <a class="ref" href="rvsum_1.html#T104" title="RVSUM_1:th.104">RVSUM_1:104</a></i>
;<br/><br/>


</div><b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c18">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:9_1_2"/><i><font color="Green" title="E13">A14</font></i>: 
<font color="Maroon" title="c18">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c14">p0</font>
 ;<br/><a NAME="E2:9_1_2"/><b>then </b>
<font color="Maroon" title="c18">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon" title="c16">t</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c18">i</font></span>)</span> = 
<font color="Maroon" title="c16">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c18">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E1:9_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="scpinvar.html#E2:9_1"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="scpinvar.html#E11"><i><font color="Green" title="E6">Lm2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c12">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> <font color="Maroon" title="c18">i</font></span>)</span>
<b>by </b><i><a class="txt" href="scpinvar.html#E3:9_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="scpinvar.html#E1:9_1_2"><i><font color="Green" title="E13">A14</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:9"/>
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9" title="SCMPDS_4:func.9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c12">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>  <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">Sum</a> <font color="Maroon" title="c15">f</font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c12">s</font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&lt;0</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,2,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5" title="SCMPDS_4:func.5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c12">s</font> )
 <b>by </b><i><a class="txt" href="scpinvar.html#E1:9"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="scpinvar.html#E12"><i><font color="Green" title="E7">Lm3</font></i></a>, <a class="ref" href="scpinvar.html#T8" target="_self" title="SCPINVAR:th.8">Th8</a></i>;<br/>


</div>
