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<b>let </b><font color="Maroon">t</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">f</font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>





<b>set </b><font color="Maroon">x</font> = <font color="Maroon">f</font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">t</font>;<br/>
<a NAME="E1:39"/><i><font color="Green">E41</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">t</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<b>set </b><font color="Maroon">DB</font> =  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>;<br/>
<b>set </b><font color="Maroon">DI</font> =  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span>;<br/>
<a NAME="E2:39"/><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">I</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">I</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/>;<br/>
<b>assume </b><a NAME="E3:39"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:39"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">I</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">t</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E6:39"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">y</font> <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">I</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">t</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:39"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:39"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="ami_3.html#D13">AMI_3:def 13</a></i>;<br/>
<a NAME="E9:39"/><b>then </b>
not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmfsa_2.html#T85">SCMFSA_2:85</a></i>;<br/>
<a NAME="E10:39"/><b>then </b>
<font color="Maroon">y</font> <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="scmbsort.html#T3" target="_self">Th3</a>, <a class="txt" href="scmbsort.html#E1:39"><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="E11:39"/><b>then </b>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0 or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E12:39"/>
contradiction
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmfsa_2.html#T82">SCMFSA_2:82</a>, <a class="ref" href="scmfsa_2.html#T83">SCMFSA_2:83</a></i>;<br/>


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