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

<a NAME="E1:19_1_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 3 &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 4 )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E2:19_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_2.html#M2">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  holds <br/>( ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K5">SubFrom</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K6">MultBy</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> ) ) &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> implies ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K3">*&gt;</a></span> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K7">Divide</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> ) ) )
 ;<br/>


</div>
