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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: MONOID_0:1</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">f</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">D</font> holds <br/> ( <font color="Olive" title="b2">f</font> is  <a href="monoid_0.html#V5" title="MONOID_0:attr.5">invertible</a>  iff ( <font color="Olive" title="b2">f</font> is  <a href="monoid_0.html#V3" title="MONOID_0:attr.3">left-invertible</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="monoid_0.html#V4" title="MONOID_0:attr.4">right-invertible</a>  ) )</div></div>
