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

<b>set </b><font color="Maroon">IT</font> =  <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font>;<br/>
<a NAME="E1:35_1_1"/><i><font color="Green">E36</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="numbers.html#K5">NAT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="ami_1.html#U1">Instruction-Counter</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span> &amp; the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p3"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> )
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">Ok</font> = the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>;<br/>
<a NAME="E2:35_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E3:35_1_1"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:35_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<i><font color="Green">E40</font></i>: the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><span class="p4"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p4"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> 
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> 
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="numbers.html#K5">NAT</a> 
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>
<b>thus </b><a NAME="E6:35_1_1"/><i><font color="Green">E41</font></i>: 
 <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font> is <a href="ami_1.html#V5">IC-Ins-separated</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:35_1_1_2"/>
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:35_1_1"/>
 <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font> is <a href="ami_1.html#V8">definite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a><br/>

<a NAME="E1:35_1_1_3"/>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:35_1_1_3"/><b>then </b>
( <font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E3:35_1_1_3"/><b>then </b><i><font color="Green">E64</font></i>: 
not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>thus </b> <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default"><span class="p4"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p4"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="pre_circ.html#K2">--&gt;</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>,<span class="p3"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:35_1_1"/>
 <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font> is <a href="ami_1.html#V10">realistic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1_1_4"/>
the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D21">AMI_1:def 21</a><br/>

<b>hence </b><a NAME="E2:35_1_1_4"/>
contradiction
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E9:35_1_1"/>
 <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font> is <a href="ami_1.html#V7">steady-programmed</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_5"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>, <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span><b> such that </b><br/><a NAME="E2:35_1_1_5"/><i><font color="Green">E66</font></i>: 
for <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">s</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p3">(<span class="default"><font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E3:35_1_1_5"/><i><font color="Green">E67</font></i>: 
the <a href="ami_1.html#U6">Execution</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a><br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>;<br/><b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>;<br/>





<a NAME="E4:35_1_1_5"/>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:35_1_1_5"/><b>then </b>
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K5">NAT</a> 
 
;<br/>
<a NAME="E6:35_1_1_5"/><b>then </b>
not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:35_1_1_5"/><b>then </b><i><font color="Green">E68</font></i>: 
not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_1_5_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> or <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_5_1_1"><b>suppose </b></a><a NAME="E1:35_1_1_5_1_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:35_1_1_5_1_1"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_5_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_1_1_5_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:35_1_1_5_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E3:35_1_1_5_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:35_1_1_5_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/></div><b>end;</b></div><b>then </b><i><font color="Green">E71</font></i>: the <a href="ami_1.html#U6">Execution</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="ordinal1.html#K1">succ</a> <span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_5_1_2"><b>suppose </b></a><a NAME="E1:35_1_1_5_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:35_1_1_5_1_2"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:35_1_1_5_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><b>then </b><i><font color="Green">E85</font></i>: the <a href="ami_1.html#U6">Execution</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">0,0</span><a href="domain_1.html#K1">]</a></span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p4">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><b>thus </b><a NAME="E5:35_1_1_5_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="ami_1.html#D12">AMI_1:def 12</a><br/>

<b>assume </b><a NAME="E10:35_1_1"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">the <a href="ami_1.html#U4">Instructions</a> of <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E11:35_1_1"/><b>then </b>
the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">the <a href="ami_1.html#U4">Instructions</a> of <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E12:35_1_1"/><b>then </b><i><font color="Green">E87</font></i>: 
the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U4">Instructions</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_6"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_1_6"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_6_1"><b>suppose </b></a><a NAME="E1:35_1_1_6_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_1_6_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_6_2"><b>suppose </b></a><a NAME="E1:35_1_1_6_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="domain_1.html#K6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:35_1_1_6_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b>the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>
;<br/><b>hence </b><a NAME="E4:35_1_1_6_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
