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<a NAME="E1:39_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">c<sub>2</sub></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">c<sub>4</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>3</sub></font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a> <font color="Olive">b<sub>2</sub></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">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="pralg_3.html#M1" target="_self">MSAlgebra-Class</a> of <font color="Maroon">c<sub>2</sub></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">c<sub>4</sub></font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:39_1_2_1"/><i><font color="Green">E29</font></i>: 
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="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:39_1_2_1"/><i><font color="Green">E30</font></i>: 
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="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>1</sub></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<sub>7</sub></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">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>hence </b><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="pralg_3.html#E1:39_1_2_1"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>6</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="pralg_3.html#E2:39_1_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="pralg_3.html#E1:39_1_2_1_1"><i><font color="Green">E31</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:39_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>6</sub></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">c<sub>2</sub></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">c<sub>4</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <font color="Olive">b<sub>3</sub></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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