<?xml version="1.0"?>
<div class="add">

<a NAME="E1:39_1_2"/>
for <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="pralg_3.html#M1" target="_self">MSAlgebra-Class</a> of <font color="Maroon">S</font>, <a href="pralg_3.html#K1" target="_self">id</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font></span>)</span>  st ( for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Olive">X</font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</font> ) &amp; ( for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Olive">Y</font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</font> ) holds <br/><font color="Olive">X</font> <a href="pboole.html#R6">=</a> <font color="Olive">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="pralg_3.html#M1" target="_self">MSAlgebra-Class</a> of <font color="Maroon">S</font>, <a href="pralg_3.html#K1" target="_self">id</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font></span>)</span>, <font color="Maroon">Y</font> be    <a href="pralg_3.html#M1" target="_self">MSAlgebra-Class</a> of <font color="Maroon">S</font>, <a href="pralg_3.html#K1" target="_self">id</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:39_1_2_1"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</font>
 <b>and </b><br/><a NAME="E2:39_1_2_1"/><i><font color="Green">E68</font></i>: 
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:39_1_2_1_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font>
 ;<br/><b>hence </b><font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> = 
<font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">Y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:39_1_2_1"/>
<font color="Maroon">X</font> <a href="pboole.html#R6">=</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:39_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="pralg_3.html#M1" target="_self">MSAlgebra-Class</a> of <font color="Maroon">S</font>, <a href="pralg_3.html#K1" target="_self">id</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font></span>)</span>  st ( for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</font> ) &amp; ( for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">EqR</font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> <font color="Olive">c</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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