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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<i><font color="Green">E13</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T37" target="_self">Th37</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T34" target="_self">Th34</a></i>
;<br/>
<a NAME="E2:32"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E3:32"/>
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> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:32_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:32_2"/><b>then </b><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="funct_1.html#E1:32"><i><font color="Green">E13</font></i></a>, <a class="txt" href="funct_1.html#E1:32_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="funct_1.html#E2:32_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#T34" target="_self">Th34</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="funct_1.html#E2:32_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#T34" target="_self">Th34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="funct_1.html#E1:32_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="funct_1.html#T34" target="_self">Th34</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:32"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="funct_1.html#E1:32"><i><font color="Green">E13</font></i></a>, <a class="txt" href="funct_1.html#E2:32"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_1.html#T9" target="_self">Th9</a></i>;<br/>


</div>
