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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: MONOID_1:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</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">a</font>, <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <span class="p1">(<span class="default"><a href="monoid_1.html#K16" title="MONOID_1:func.16">chi</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; ( <font color="Olive" title="b3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> implies <span class="p1">(<span class="default"><a href="monoid_1.html#K16" title="MONOID_1:func.16">chi</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</div></div>
