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<a NAME="E1:117_1_2"/>
for <font color="Olive">G</font>, <font color="Olive">H</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>  st ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Olive">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font> ) &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Olive">H</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font> ) holds <br/><font color="Olive">G</font> <a href="funct_2.html#R2">=</a> <font color="Olive">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>, <font color="Maroon">H</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:117_1_2_1"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E2:117_1_2_1"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:117_1_2_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="117_1_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:117_1_2_1_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Maroon">x</font>,<font color="Maroon">X</font>
<b>by </b><i>, <a class="txt" href="modelc_1.html#E32"><i><font color="Green">Lemma95</font></i></a></i>
<br/>.= 
<font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E3:117_1_2_1_1"/>
<font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:117_1_2_1"/>
<font color="Maroon">G</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:117_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>  st ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font> ) &amp; ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K47" target="_self">F_LABEL</a> <font color="Olive">x</font>,<font color="Maroon">X</font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/>


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