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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: CAT_5:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</font> being   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font><br/>  for <font color="Olive" title="b3">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="cat_5.html#K12" title="CAT_5:func.12">-SliceCat</a> <font color="Olive" title="b1">C</font></span>)</span> holds <br/> ( <font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K8" title="CAT_2:func.8">[</a><span class="default"><span class="p2"><a href="cat_2.html#K8" title="CAT_2:func.8">[</a><span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a></span>)</span></span><a href="cat_2.html#K8" title="CAT_2:func.8">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a></span>)</span></span><a href="cat_2.html#K8" title="CAT_2:func.8">]</a></span> &amp;  <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K4" title="GRAPH_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K16" title="CAT_5:func.16">`2</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">(*)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  &amp;  <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> <a href="cat_5.html#K17" title="CAT_5:func.17">`11</a>  &amp;  <a href="graph_1.html#K4" title="GRAPH_1:func.4">cod</a> <font color="Olive" title="b3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> <a href="cat_5.html#K18" title="CAT_5:func.18">`12</a>  )</div></div>
