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<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c2">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/>



<a NAME="E1:9"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">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="ref" href="ami_1.html#T96" title="AMI_1:th.96">AMI_1:96</a></i>;<br/>
<a NAME="E2:9"/><i><font color="Green" title="E11">A2</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa_5.html#T5" target="_self" title="SCMFSA_5:th.5">Th5</a></i>;<br/>
<a NAME="E3:9"/><i><font color="Green" title="E12">A3</font></i>: 
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">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#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</font>
 
<b>by </b><i><a class="ref" href="scmfsa_5.html#T6" target="_self" title="SCMFSA_5:th.6">Th6</a></i>;<br/>
<a NAME="E4:9"/>
 <a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E2:9"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="ami_1.html#D43" title="AMI_1:def.43">AMI_1:def 43</a></i>;<br/>
<a NAME="E5:9"/><b>then </b><i><font color="Green" title="E13">A4</font></i>: 
<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="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>
 
<b>by </b><i><a class="txt" href="scmfsa_5.html#E2:9"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="scmfsa_5.html#E3:9"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/>
<b>thus </b><a NAME="E6:9"/>
 <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:9_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K26" title="AMI_1:func.26">Start-At</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K27" title="AMI_1:func.27">IC</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="scmfsa_4.html#K1" title="SCMFSA_4:func.1">+</a> <font color="Maroon" title="c2">k</font></span>)</span>
 ;<br/>

<b>hence </b><a NAME="E2:9_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmfsa_5.html#K1" title="SCMFSA_5:func.1">Relocated</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">k</font>
 <b>by </b><i><a class="txt" href="scmfsa_5.html#E1:9"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="scmfsa_5.html#E5:9"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>


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


</div>
