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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th13</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: MODCAT_1:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">UN</font> being   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a><br/>  for <font color="Olive" title="b2">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K11" title="MODCAT_1:func.11">LModCat</a> (<font color="Olive" title="b1">UN</font>,<font color="Olive" title="b2">R</font>)</span>)</span><br/>  for <font color="Olive" title="b4">f9</font> being    <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> (<font color="Olive" title="b1">UN</font>,<font color="Olive" title="b2">R</font>)</span>)</span>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f9</font> holds <br/>(  <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b4">f9</font> &amp;  <a href="graph_1.html#K4" title="GRAPH_1:func.4">cod</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Olive" title="b4">f9</font> )</div></div>
