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



<b>given </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:82"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setwiseo.html#D2">SETWISEO:def 2</a><br/>

<a NAME="E2:82"/>
( <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a>  <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> )
 
<b>by </b><i><a class="txt" href="monoid_1.html#E1:82"><i><font color="Green">E50</font></i></a>, <a class="ref" href="monoid_1.html#T53" target="_self">Th53</a>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:82"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a>  <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a>  &amp;  <a href="binop_1.html#K3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K21" target="_self">.:^2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 ;<br/>


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