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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th52</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: MONOID_1:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">o</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">D</font>  st <font color="Olive" title="b3">a</font> <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Olive" title="b2">o</font> holds <br/>( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">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="Olive" title="b2">o</font> <a href="monoid_1.html#K19" title="MONOID_1:func.19">.:^2</a>  &amp; <font color="Olive" title="b2">o</font> <a href="monoid_1.html#K19" title="MONOID_1:func.19">.:^2</a>  is  <a href="setwiseo.html#V1" title="SETWISEO:attr.1">having_a_unity</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="Olive" title="b2">o</font> <a href="monoid_1.html#K19" title="MONOID_1:func.19">.:^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="Olive" title="b3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</div></div>
