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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>;<br/>



<b>given </b><font color="Maroon" title="c3">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><b> such that </b><a NAME="E1:82"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">o</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setwiseo.html#D2" title="SETWISEO:def.2">SETWISEO:def 2</a><br/>

<a NAME="E2:82"/>
( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a>  <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">o</font> &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<b>by </b><i><a class="txt" href="monoid_1.html#E1:82"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="monoid_1.html#T53" target="_self" title="MONOID_1:th.53">Th53</a>, <a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E3:82"/>
( <font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a>  <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">o</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a>  &amp;  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">o</font> <a href="monoid_1.html#K21" title="MONOID_1:func.21">.:^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon" title="c2">o</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 ;<br/>


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