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

<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="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="finseqop.html#NR2" target="_self">has_an_inverseOp</a>  )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E2:75"/>
<font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="finseqop.html#E1:75"><i><font color="Green">E34</font></i></a>, <a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>;<br/>
<b>hence </b><a NAME="E3:75"/>
<span class="p1">(<span class="default"><a href="finseqop.html#K6" target="_self">the_inverseOp_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseqop.html#E1:75"><i><font color="Green">E34</font></i></a>, <a class="ref" href="finseqop.html#T64" target="_self">Th64</a></i>;<br/>


</div>
