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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="valuat_1.html#M1">interpretation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:43"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:43"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="calcul_1.html#R9" target="_self">|=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E3:43"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="calcul_1.html#R6" target="_self">|=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="calcul_1.html#D14" target="_self">Def14</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="calcul_1.html#D11" target="_self">CALCUL_1:def 11</a>,<a class="ref" href="calcul_1.html#D14" target="_self">CALCUL_1:def 14</a><br/>

<b>assume </b><a NAME="E4:43"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:43"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="calcul_1.html#E4:43"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<a NAME="E7:43"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E3:43"><i><font color="Green">E42</font></i></a>, <a class="txt" href="calcul_1.html#E4:43"><i><font color="Green">E43</font></i></a>, <a class="ref" href="calcul_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E8:43"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E6:43"><i><font color="Green">E44</font></i></a>, <a class="ref" href="calcul_1.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E9:43"/><b>then </b>
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="calcul_1.html#K3" target="_self">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E10:43"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="calcul_1.html#E1:43"><i><font color="Green">E41</font></i></a>, <a class="ref" href="relat_1.html#T188">RELAT_1:188</a></i>;<br/>
<b>hence </b><a NAME="E11:43"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="calcul_1.html#E7:43"><i><font color="Green">E45</font></i></a>, <a class="ref" href="sublemma.html#T70">SUBLEMMA:70</a></i>;<br/>


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