<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th11</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: MODCAT_1:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being    <a href="modcat_1.html#M1" title="MODCAT_1:mode.1">LeftMod_DOMAIN</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">f</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> <font color="Olive" title="b2">V</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">g</font>,<font color="Olive" title="b4">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> <span class="p1">(<span class="default"><a href="modcat_1.html#K10" title="MODCAT_1:func.10">comp</a> <font color="Olive" title="b2">V</font></span>)</span> iff  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Olive" title="b3">g</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">f</font> )</div></div>
