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

<b>let </b><font color="Maroon">p</font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<a NAME="E1:32"/><i><font color="Green">E24</font></i>: 
 <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T35">AMI_5:35</a></i>;<br/>
<a NAME="E2:32"/><i><font color="Green">E27</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span>
 
<b>by </b><i><a class="txt" href="reloc.html#E2:32"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E3:32"/><i><font color="Green">E46</font></i>: 
 <a href="ami_3.html#K13">IC</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="reloc.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E4:32"/>
 <a href="ami_3.html#K13">IC</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="reloc.html#T3" target="_self">Th3</a>, <a class="ref" href="ami_3.html#D16">AMI_3:def 16</a></i>;<br/>
<a NAME="E5:32"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font>
 
<b>by </b><i><a class="ref" href="reloc.html#T3" target="_self">Th3</a>, , <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/>
<b>thus </b><a NAME="E6:32"/>
 <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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><br/>

<b>assume </b><a NAME="E1:32_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K13">IC</a> <font color="Maroon">p</font></span>)</span> <a href="reloc.html#K1" target="_self">+</a> <font color="Maroon">k</font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E2:32_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="reloc.html#K6" target="_self">Relocated</a> <font color="Maroon">p</font>,<font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="reloc.html#D3" target="_self">Def3</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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


</div>
