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<b>let </b><font color="Maroon" title="c1">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>







<b>set </b><font color="Maroon" title="c5">t</font> = <font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font>;<br/>
<b>set </b><font color="Maroon" title="c6">p</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font>;<br/>
<b>assume </b><a NAME="E1:46"/><i><font color="Green" title="E46">A1</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font>
 ;<br/>

<a NAME="E2:46"/><i><font color="Green" title="E47">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</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"><font color="Maroon" title="c2">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E3:46"/><b>then </b><i><font color="Green" title="E48">A3</font></i>: 
<font color="Maroon" title="c2">f</font> <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"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:46"/>
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T83" title="SCMFSA_2:th.83">SCMFSA_2:83</a></i>;<br/>
<a NAME="E5:46"/><b>then </b><i><font color="Green" title="E49">A4</font></i>: 
not  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <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"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:46"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:46"/>
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <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="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T45" title="SCMFSA6A:th.45">SCMFSA6A:45</a></i>;<br/>
<a NAME="E7:46"/><b>then </b><i><font color="Green" title="E50">A5</font></i>: 
 <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0 <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"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></i>;<br/>
<a NAME="E8:46"/>
<font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/>
<a NAME="E9:46"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:46"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K21" title="SCMFSA_2:func.21">.</a> <font color="Maroon" title="c2">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="txt" href="scmbsort.html#E3:46"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c1">w</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon" title="c3">s</font> <a href="scmfsa_2.html#K20" title="SCMFSA_2:func.20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="ami_1.html#K17" title="AMI_1:func.17">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c1">w</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E1:46"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="scmbsort.html#E7:46"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E5:46"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46" title="SCMFSA6A:th.46">SCMFSA6A:46</a></i>
;<br/>


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