<?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="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</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="E1:73"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#NR2" target="_self">has_an_inverseOp</a>  )
 ;<br/>

<a NAME="E2:73"/><b>then </b>
 <a href="finseqop.html#K6" target="_self">the_inverseOp_wrt</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#R1" target="_self">is_an_inverseOp_wrt</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="finseqop.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:73"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseqop.html#K6" target="_self">the_inverseOp_wrt</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseqop.html#K6" target="_self">the_inverseOp_wrt</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</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>3</sub></font> )
 <b>by </b><i><a class="ref" href="finseqop.html#D1" target="_self">Def1</a></i>;<br/>


</div>
