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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:40"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T46" target="_self">Th46</a></i>;<br/>
<a NAME="E2:40"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/>
<a NAME="E3:40"/><i><font color="Green">E41</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E4:40"/><i><font color="Green">E42</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:40"><i><font color="Green">E40</font></i></a>, <a class="ref" href="relat_1.html#T25">RELAT_1:25</a></i>;<br/>
<a NAME="E5:40"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E6:40"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:40"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E7:40"/><b>then </b><i><font color="Green">E44</font></i>: 
not  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:40"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>thus </b><a NAME="E8:40"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmbsort.html#E4:40"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmbsort.html#E6:40"><i><font color="Green">E43</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_3.html#D17">AMI_3:def 17</a><br/>

<b>thus </b> <a href="ami_3.html#K13">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></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="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E4:40"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmbsort.html#E6:40"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ami_3.html#D16">AMI_3:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>3</sub></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="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmbsort.html#E7:40"><i><font color="Green">E44</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46">SCMFSA6A:46</a></i>
;<br/>


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