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

<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<font color="Maroon" title="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">l1</font>, <font color="Maroon" title="c5">l2</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of <font color="Maroon" title="c3">S</font>;<br/>







<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:10_1"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
 ;<br/><a NAME="E2:10_1"/><i><font color="Green" title="E11">A2</font></i>: 
(  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> &amp;  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> )
 ;<br/><a NAME="E3:10_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:10_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/><a NAME="E4:10_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmring4.html#E2:10_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/><a NAME="E5:10_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T6" title="ZFMISC_1:th.6">ZFMISC_1:6</a></i>;<br/><a NAME="E6:10_1"/><b>then </b>
<font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E7:10_1"/><b>then </b>
<font color="Maroon" title="c4">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="scmring4.html#K1" title="SCMRING4:func.1">-'</a> <font color="Maroon" title="c1">k</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th5</a></i>;<br/><b>hence </b><a NAME="E8:10_1"/>
 <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <font color="Maroon" title="c4">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <font color="Maroon" title="c5">l2</font>
 <b>by </b><i><a class="ref" href="scmring4.html#T5" target="_self" title="SCMRING4:th.5">Th5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:10"/>
 <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <font color="Maroon" title="c4">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <font color="Maroon" title="c5">l2</font>
 ;<br/>

<a NAME="E3:10"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c4">l1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <font color="Maroon" title="c5">l2</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/>
<a NAME="E4:10"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c4">l1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c5">l2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/>
<a NAME="E5:10"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c4">l1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>,<font color="Maroon" title="c5">l2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T6" title="ZFMISC_1:th.6">ZFMISC_1:6</a></i>;<br/>
<b>hence </b><a NAME="E6:10"/>
 <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l1</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K27" title="AMI_1:func.27">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">l2</font> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c1">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>


</div>
