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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th4</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: INDEX_1:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</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="b3">F</font>, <font color="Olive" title="b4">G</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b5">I</font> being    <a href="index_1.html#M3" title="INDEX_1:mode.3">Indexing</a> of <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">G</font><br/>  for <font color="Olive" title="b6">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">B</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b5">I</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">m</font> is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1">(<span class="default"><font color="Olive" title="b5">I</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">m</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b5">I</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a></span>)</span> <a href="index_1.html#K2" title="INDEX_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">m</font></span>)</span></div></div>
