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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">g</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>set </b><font color="Maroon">a</font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<b>assume </b><a NAME="E1:36"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 ;<br/>

<b>assume </b><a NAME="E2:36"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">f</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a> <font color="Maroon">s</font>,<font color="Maroon">m</font> &amp; <font color="Maroon">g</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>,<font color="Maroon">m</font> )
 ;<br/>

<b>assume </b><a NAME="E3:36"/><i><font color="Green">E47</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> &amp; <font color="Maroon">f</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">n</font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">t</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/> for <font color="Olive">f1</font>, <font color="Olive">f2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>   st <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Olive">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Olive">f1</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a> <font color="Olive">t</font>,<font color="Maroon">m</font> &amp; <font color="Olive">f2</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Olive">t</font>,<font color="Maroon">m</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">f2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">f1</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">f1</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">a<sub>1</sub></font> holds <br/>( <font color="Olive">f1</font>,<font color="Olive">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Olive">f2</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">f1</font> holds <br/><font color="Olive">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 holds <br/> ex <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> ) ) );<br/>
<a NAME="E4:36"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">f2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>



<b>assume </b><a NAME="E1:36_1"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; 0 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Maroon">f1</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">m</font> &amp; <font color="Maroon">f2</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">m</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">f1</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,0 )
 ;<br/>

<b>then </b><i><font color="Green">E54</font></i>: <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,6</span>)</span> = 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
0
<b>by </b><i/>
;<br/>
<div><i><font color="Green">E81</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_1_2"/><i><font color="Green">E82</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_8.html#T23">SCMPDS_8:23</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E4:36_1"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>
<b>thus </b><a NAME="E5:36_1"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>

<b>thus </b><a NAME="E6:36_1"/>
<font color="Maroon">f2</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E7:36_1"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E8:36_1"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="nat_1.html#K1">+</a> 1 holds <br/> ex <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E84</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">f2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1"/><i><font color="Green">E91</font></i>: 
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Maroon">f1</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">m</font> &amp; <font color="Maroon">f2</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">m</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f1</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><b>set </b><font color="Maroon">Bt</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>;<br/><b>set </b><font color="Maroon">x</font> =  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">y</font> =  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0;<br/><a NAME="E2:36_2_1"/><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i/>;<br/><i><font color="Green">E93</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> = 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i/>
<br/>.= 
 <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/><a NAME="E4:36_2_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i/>;<br/><a NAME="E5:36_2_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 ;<br/><i><font color="Green">E96</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0 = 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>
<br/>.= 
 <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/><a NAME="E7:36_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E8:36_2_1"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E9:36_2_1"/><i><font color="Green">E98</font></i>: 
( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7 &amp; <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Olive">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">i</font></span>)</span> ) &amp; ( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) &amp; ( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> <a href="hidden.html#R1">=</a> 0 ) ) )
 <b>by </b><i>, </i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3"/>
( <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> or <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
 ;<br/><div class="add"><b>consider </b><font color="Maroon">h</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:36_2_1_3_1"/><i><font color="Green">E100</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> holds <br/><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Olive">i</font></span>)</span></span>)</span> ) )
 <b>by </b><i/>;<br/><a NAME="E4:36_2_1_3_1"/><i><font color="Green">E101</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E5:36_2_1_3_1"/><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 6</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E6:36_2_1_3_1"/><i><font color="Green">E103</font></i>: 
<font color="Maroon">h</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> )
 ;<br/><b>hence </b><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div><a NAME="E8:36_2_1_3_1"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">f2</font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span>,<font color="Maroon">m</font>
 <b>by </b><i/>;<br/><a NAME="E9:36_2_1_3_1"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E10:36_2_1_3_1"/><b>then </b><i><font color="Green">E105</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><div><i><font color="Green">E106</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_2"/><i><font color="Green">E107</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><a NAME="E2:36_2_1_3_1_2"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:36_2_1_3_1_2"/><b>then </b><i><font color="Green">E111</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:36_2_1_3_1_2"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E5:36_2_1_3_1_2"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 <b>by </b><i>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a></i>;<br/><b>thus </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, , </i>
<br/>.= 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_3"/><i><font color="Green">E114</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 ;<br/><a NAME="E2:36_2_1_3_1_3"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E3:36_2_1_3_1_3"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E4:36_2_1_3_1_3"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:36_2_1_3_1_3"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:36_2_1_3_1_3"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E7:36_2_1_3_1_3"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font>
 <b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:36_2_1_3_1_3"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E9:36_2_1_3_1_3"/><b>then </b><i><font color="Green">E120</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, </i>;<br/><a NAME="E10:36_2_1_3_1_3"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E11:36_2_1_3_1_3"/><b>then </b>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="scpisort.html#T4" target="_self">Th4</a></i>;<br/><b>hence </b><a NAME="E12:36_2_1_3_1_3"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, , <a class="txt" href="scpisort.html#E4:36"><i><font color="Green">E52</font></i></a>, <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E13:36_2_1_3_1"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">h</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/><a NAME="E14:36_2_1_3_1"/><b>then </b><i><font color="Green">E122</font></i>: 
( <font color="Maroon">h</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">f2</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> holds <br/><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 holds <br/> ex <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> ) ) )
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a></i>;<br/><a NAME="E15:36_2_1_3_1"/><i><font color="Green">E123</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E16:36_2_1_3_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E17:36_2_1_3_1"/><b>then </b><i><font color="Green">E127</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E18:36_2_1_3_1"/><i><font color="Green">E128</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E19:36_2_1_3_1"/><b>then </b><i><font color="Green">E131</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E20:36_2_1_3_1"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
 <b>by </b><i>, , , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="scpisort.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E21:36_2_1_3_1"/><b>then </b><i><font color="Green">E133</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i>, , <a class="ref" href="scpisort.html#T4" target="_self">Th4</a>, <a class="txt" href="scpisort.html#E4:36"><i><font color="Green">E52</font></i></a>, </i>;<br/><a NAME="E22:36_2_1_3_1"/><i><font color="Green">E134</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="scpisort.html#T4" target="_self">Th4</a>, </i>;<br/><a NAME="E23:36_2_1_3_1"/><b>then </b><i><font color="Green">E135</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, </i>;<br/><a NAME="E24:36_2_1_3_1"/><b>then </b>
<font color="Maroon">f1</font>,<font color="Maroon">h</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, <a class="ref" href="scpisort.html#T4" target="_self">Th4</a>, <a class="txt" href="scpisort.html#E4:36"><i><font color="Green">E52</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E25:36_2_1_3_1"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="rfinseq.html#T2">RFINSEQ:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_4"/><i><font color="Green">E136</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_1_4_1"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_3_1_4_1_1"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E3:36"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_2"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_1_4_1_2_1_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_2_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_3_1_4_1_2_1_1_1"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_2_1_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font>
 ;<br/><div class="add"><a NAME="E2:36_2_1_3_1_4_1_2_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:36_2_1_3_1_4_1_2_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>then consider </b><font color="Maroon">mm</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:36_2_1_3_1_4_1_2_1_1_2"/><i><font color="Green">E138</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">mm</font> &amp; <font color="Maroon">mm</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">mm</font> )
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scpisort.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E6:36_2_1_3_1_4_1_2_1_1_2"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, , , </i>;<br/><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_1_4_1_2_1_1_2_1_1"/>
( <font color="Maroon">mm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">mm</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_2_1_1_2_1_1_1"/>
<font color="Maroon">mm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_3_1_4_1_2_1_1_2_1_1_1"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_4_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/><i><font color="Green">E140</font></i>: 
<font color="Maroon">mm</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon">mm</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">mm</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font>
 <b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E142</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">mm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">mm</font>
 <b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, , , <a class="ref" href="scpisort.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E5:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="scpisort.html#T2" target="_self">Th2</a>, , , </i>;<br/><b>hence </b><a NAME="E6:36_2_1_3_1_4_1_2_1_1_2_1_1_2"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E27:36_2_1_3_1"/>
<font color="Maroon">f2</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_5"/><i><font color="Green">E143</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><a NAME="E2:36_2_1_3_1_5"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E3:36_2_1_3_1_5"/><b>then </b><i><font color="Green">E146</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:36_2_1_3_1_5"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:36_2_1_3_1_5"/><b>then </b><i><font color="Green">E147</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, </i>
<br/>.= 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, <a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, , </i>
;<br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_1_6"/><i><font color="Green">E148</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_1_6_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_6_1_1"/><i><font color="Green">E149</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon">j</font> = <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1;<br/><b>thus </b><a NAME="E2:36_2_1_3_1_6_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b><a NAME="E3:36_2_1_3_1_6_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b><a NAME="E4:36_2_1_3_1_6_1_1"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_6_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:36_2_1_3_1_6_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="scpisort.html#T5" target="_self">Th5</a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:36_2_1_3_1_6_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>then consider </b><font color="Maroon">mm</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:36_2_1_3_1_6_1_2"/><i><font color="Green">E151</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">mm</font> &amp; <font color="Maroon">mm</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">mm</font> )
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, , <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E2:36"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scpisort.html#T5" target="_self">Th5</a></i>;<br/><div><b>hereby </b>
<div class="add"><a NAME="E1:36_2_1_3_1_6_1_2_1"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_1_6_1_2_1_1"/>
( <font color="Maroon">mm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">mm</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_6_1_2_1_1_1"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">mm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon">j</font> = <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2;<br/><b>thus </b><a NAME="E2:36_2_1_3_1_6_1_2_1_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b><a NAME="E3:36_2_1_3_1_6_1_2_1_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>thus </b><a NAME="E4:36_2_1_3_1_6_1_2_1_1_1"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="ref" href="scpisort.html#T4" target="_self">Th4</a>, <a class="txt" href="scpisort.html#E4:36"><i><font color="Green">E52</font></i></a>, , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_1_6_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_1_6_1_2_1_1_2"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">mm</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:36_2_1_3_1_6_1_2_1_1_2"/>
<font color="Maroon">mm</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:36_2_1_3_1_6_1_2_1_1_2"/><b>then </b><i><font color="Green">E211</font></i>: 
<font color="Maroon">mm</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>take </b><font color="Maroon">mm</font> = <font color="Maroon">mm</font>;<br/><b>thus </b><a NAME="E4:36_2_1_3_1_6_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">mm</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E5:36_2_1_3_1_6_1_2_1_1_2"/>
<font color="Maroon">mm</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><b>thus </b><a NAME="E6:36_2_1_3_1_6_1_2_1_1_2"/>
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">mm</font>
 <b>by </b><i><a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, , , , <a class="ref" href="scpisort.html#T6" target="_self">Th6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_2"/><i><font color="Green">E212</font></i>: 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
 ;<br/><div class="add"><div><i><font color="Green">E213</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_2_1"/><i><font color="Green">E214</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> )
 ;<br/><a NAME="E2:36_2_1_3_2_1"/><b>then </b>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:36_2_1_3_2_1"/><b>then </b><i><font color="Green">E215</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:36_2_1_3_2_1"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><i><font color="Green">E217</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,6</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
0
<b>by </b><i>, , </i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_2_1_2"/>
( <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 or <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> or ( <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_1_2_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_1_2_1"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><div class="add"><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>
<b>by </b><i>, , , , , , <a class="ref" href="scmpds_8.html#T23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_1_2_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_1_2_2"/><i><font color="Green">E219</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
<b>by </b><i>, , , , , , <a class="ref" href="scmpds_8.html#T23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_1_2_3"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_1_2_3"/>
( <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span> )
 ;<br/><div class="add"><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_8.html#T23">SCMPDS_8:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E3:36_2_1_3_2"/><b>then </b><i><font color="Green">E220</font></i>: 
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/><b>thus </b><a NAME="E4:36_2_1_3_2"/>
<font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_3_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:36_2_1_3_2_2"/><i><font color="Green">E221</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_2_2_1"/>
( <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_2_1_1"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_3_2_2_1_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_2_1_2"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2_1_3_2_2_1_2_1_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_2_1_2_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_3_2_2_1_2_1_1_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_3_2_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:36_2_1_3_2_2_1_2_1_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font>
 ;<br/><div class="add"><a NAME="E2:36_2_1_3_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:36_2_1_3_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:36_2_1_3_2_2_1_2_1_1_2"/><b>then </b><i><font color="Green">E223</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="txt" href="scpisort.html#E2"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/><a NAME="E5:36_2_1_3_2_2_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:36_2_1_3_2_2_1_2_1_1_2"/><b>then </b><i><font color="Green">E224</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E7:36_2_1_3_2_2_1_2_1_1_2"/><i><font color="Green">E225</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E8:36_2_1_3_2_2_1_2_1_1_2"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font>
 <b>by </b><i>, , <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E9:36_2_1_3_2_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span></span>)</span>,0</span>)</span>
 <b>by </b><i>, , , <a class="ref" href="scpisort.html#T1" target="_self">Th1</a>, </i>;<br/><b>hence </b><a NAME="E10:36_2_1_3_2_2_1_2_1_1_2"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="txt" href="scpisort.html#E1:36"><i><font color="Green">E44</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:36_2_1_3_2"/>
<font color="Maroon">f2</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/><b>thus </b><a NAME="E7:36_2_1_3_2"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/><b>thus </b><a NAME="E8:36_2_1_3_2"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/> ex <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:36_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E6:36"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i>
<b>hence </b><a NAME="E7:36"/>
( <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">g</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> ) &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 holds <br/> ex <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> ) ) )
 <b>by </b><i>, , </i>;<br/>


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