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<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>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="binop_1.html#NM1">UnOp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:102"/><i><font color="Green">E49</font></i>: 
( <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="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#NR2" target="_self">has_an_inverseOp</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a>  <a href="finseqop.html#K6" target="_self">the_inverseOp_wrt</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseqop.html#K8" target="_self">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <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>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>3</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>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseqop.html#T87" target="_self">Th87</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="finseqop.html#E1:102"><i><font color="Green">E49</font></i></a>, <a class="ref" href="setwiseo.html#T23">SETWISEO:23</a></i>
;<br/>


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