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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th44</font></span>: <a NAME="T44"><span class="comment"><font color="firebrick">:: MONOID_1:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font>, <font color="Olive" title="b3">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="b4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">D1</font>,<font color="Olive" title="b2">D2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Olive" title="b3">D</font><br/>  for <font color="Olive" title="b5">X1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">D1</font><br/>  for <font color="Olive" title="b6">X2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b2">D2</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="monoid_1.html#K19" title="MONOID_1:func.19">.:^2</a></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b5">X1</font>,<font color="Olive" title="b6">X2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b5">X1</font>,<font color="Olive" title="b6">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></div></div>
