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<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E1:18"/><i><font color="Green">E26</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 ;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">k</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E2:18"/><i><font color="Green">E28</font></i>: 
 <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E3:18"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:18_1"/>
<font color="Maroon">c</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span>
 ;<br/><a NAME="E2:18_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T29">SCMFSA_7:29</a></i>;<br/><a NAME="E3:18_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T26">SCMFSA_7:26</a></i>;<br/><font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmfsa_7.html#D1">SCMFSA_7:def 1</a></i>
;<br/><b>hence </b><a NAME="E5:18_1"/>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:18"/><b>then </b>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:18"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">i</font>
 ;<br/>


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