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<div class="add">

<b>let </b><font color="Maroon" title="c1">l1</font>, <font color="Maroon" title="c2">l2</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:36_1"/><i><font color="Green" title="E20">A1</font></i>: 
 <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span>
 ;<br/><a NAME="E2:36_1"/><i><font color="Green" title="E21">A2</font></i>: 
(  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span> &amp;  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span> )
 ;<br/><a NAME="E3:36_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E1:36_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="ami_5.html#T35" title="AMI_5:th.35">AMI_5:35</a></i>;<br/><a NAME="E4:36_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="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E2:36_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="ami_5.html#T35" title="AMI_5:th.35">AMI_5:35</a></i>;<br/><a NAME="E5:36_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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="E6:36_1"/><b>then </b>
<font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">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="E7:36_1"/><b>then </b>
<font color="Maroon" title="c1">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="scmpds_3.html#K4" title="SCMPDS_3:func.4">-'</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T34" target="_self" title="SCMPDS_3:th.34">Th34</a></i>;<br/><b>hence </b><a NAME="E8:36_1"/>
 <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c1">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c2">l2</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T34" target="_self" title="SCMPDS_3:th.34">Th34</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:36"/>
 <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c1">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c2">l2</font>
 ;<br/>

<a NAME="E3:36"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c1">l1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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_3.html#K12" title="AMI_3:func.12">Start-At</a> <font color="Maroon" title="c2">l2</font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T35" title="AMI_5:th.35">AMI_5:35</a></i>;<br/>
<a NAME="E4:36"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c1">l1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T35" title="AMI_5:th.35">AMI_5:35</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c1">l1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</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="E6:36"/>
 <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">l1</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K12" title="AMI_3:func.12">Start-At</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l2</font> <a href="scmpds_3.html#K3" title="SCMPDS_3:func.3">+</a> <font color="Maroon" title="c3">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/>


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