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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: MODCAT_1:12</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>, <font color="Olive" title="b4">g</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> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">g</font>,<font color="Olive" title="b3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</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> iff  <a href="graph_1.html#K3" title="GRAPH_1:func.3">dom</a> <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K4" title="GRAPH_1:func.4">cod</a> <font color="Olive" title="b3">f</font> )</div></div>
