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

<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">o</font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">o</font> is <a href="binop_1.html#V1" target="_self">commutative</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:16_1"/>
( ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds <br/> ( <font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Maroon">e</font>,<font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Olive">a</font>,<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> ) ) implies for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Olive">a</font>,<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> )
 ;<br/><b>assume </b><a NAME="E2:16_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Olive">a</font>,<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font>
 ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/><b>thus </b><font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Maroon">e</font>,<font color="Maroon">a</font> = 
<font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">e</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a</font>
<b>by </b><i/>
;<br/><b>thus </b><a NAME="E4:16_1"/>
<font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
( <font color="Maroon">e</font> <a href="binop_1.html#R3" target="_self">is_a_unity_wrt</a> <font color="Maroon">o</font> iff for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">o</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Olive">a</font>,<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> )
 <b>by </b><i/>;<br/>


</div>
