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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>





<b>assume </b><a NAME="E1:84"/><i><font color="Green">E52</font></i>: 
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 ;<br/>

<a NAME="E2:84"/><i><font color="Green">E53</font></i>: 
(  <a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p5">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">y0</font> being   <a href="qc_lang1.html#NM3">bound_QC-variable</a><b> such that </b><br/><a NAME="E4:84"/><i><font color="Green">E54</font></i>: 
not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="calcul_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E5:84"/>
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T9" target="_self">Th9</a>, <a class="ref" href="calcul_1.html#T10" target="_self">Th10</a>, <a class="txt" href="calcul_1.html#E11:84"><i><font color="Green">E56</font></i></a></i>;<br/>
<a NAME="E6:84"/><b>then </b>
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:84"/><b>then </b>
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E8:84"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">f1</font> = <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<a NAME="E9:84"/>
not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T11" target="_self">Th11</a>, </i>;<br/>
<a NAME="E10:84"/><b>then </b>
( not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">f</font> &amp; not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E11:84"/><b>then </b><i><font color="Green">E56</font></i>: 
( not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> &amp;  <a href="calcul_1.html#K2" target="_self">Suc</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font> &amp; not <font color="Maroon">y0</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="calcul_1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E12:84"/>
 <a href="calcul_1.html#R4" target="_self">|-</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" target="_self">Ant</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="substut2.html#K4">.</a> <font color="Maroon">x</font>,<font color="Maroon">y0</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="calcul_1.html#T12" target="_self">Th12</a>, <a class="ref" href="calcul_1.html#T13" target="_self">Th13</a>, <a class="ref" href="calcul_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E13:84"/>
 <a href="calcul_1.html#R4" target="_self">|-</a> <font color="Maroon">f</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i/>;<br/>


</div>
