<?xml version="1.0"?>
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<b>let </b><font color="Maroon">z</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<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/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of 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>;<br/>







<a NAME="E1:41"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">z</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E2:41"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green">E39</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<b>set </b><font color="Maroon">M</font> =  <a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font>;<br/>
<b>set </b><font color="Maroon">F</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Olive">s</font></span>)</span></span>)</span> where <font color="Olive">s</font> is   <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> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp; <font color="Olive">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> ) </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:41_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Olive">s</font></span>)</span></span>)</span> where <font color="Olive">s</font> is   <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> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp; <font color="Olive">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">s</font> being   <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><b> such that </b><br/><a NAME="E3:41_1_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">s</font></span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 ;<br/><a NAME="E4:41_1_1"/><i><font color="Green">E41</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, </i>;<br/><font color="Maroon">y</font> = 
 <a href="ordinal1.html#K1">succ</a> <font color="Maroon">z</font>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">z</font> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, <a class="ref" href="card_1.html#T52">CARD_1:52</a></i>
;<br/><b>hence </b><a NAME="E6:41_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:41_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><b>then </b><i><font color="Green">E64</font></i>: <font color="Maroon">y</font> = 
<font color="Maroon">z</font> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
 <a href="ordinal1.html#K1">succ</a> <font color="Maroon">z</font>
<b>by </b><i>, <a class="ref" href="card_1.html#T52">CARD_1:52</a></i>
;<br/><b>consider </b><font color="Maroon">w</font> being   <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>;<br/><b>set </b><font color="Maroon">f</font> = 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="pre_circ.html#K2">--&gt;</a> <font color="Maroon">i</font>;<br/><a NAME="E5:41_1"/><i><font color="Green">E66</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</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> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">i</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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">w</font> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</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> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">i</font></span>)</span> as   <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> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">l'</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M1">Element</a> of  <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><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/><b>set </b><font color="Maroon">u</font> = <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="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font>;<br/><b>set </b><font color="Maroon">t</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span>;<br/><a NAME="E8:41_1"/><i><font color="Green">E67</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E9:41_1"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="ami_1.html#K2">IC</a> <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#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><i><font color="Green">E69</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <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> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span> <a href="funct_1.html#K1">.</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>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">z</font>
<b>by </b><i>, <a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/><a NAME="E11:41_1"/>
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <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#T48">AMI_1:48</a></i>;<br/><a NAME="E12:41_1"/><b>then </b>
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"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <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> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> = 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="ami_1.html#U2">Instruction-Locations</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> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">i</font></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#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><a NAME="E14:41_1"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8">CurInstr</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p5">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, , </i>;<br/><a NAME="E15:41_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p5">(<span class="default"><a href="amistd_1.html#K4" target="_self">STC</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="ami_1.html#K15">.--&gt;</a> <font color="Maroon">l'</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">z</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E16:41_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Olive">s</font></span>)</span></span>)</span> where <font color="Olive">s</font> is   <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> : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp; <font color="Olive">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> ) </span>}</span> 
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:41"/>
 <a href="amistd_1.html#K1" target="_self">NIC</a> <font color="Maroon">i</font>,<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
