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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E36">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: RINGCAT1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="ringcat1.html#NM3" title="RINGCAT1:NM.3">Ring_DOMAIN</a><br/>  for <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">f</font> being    <a href="ringcat1.html#M3" title="RINGCAT1:mode.3">Element</a> of  <a href="ringcat1.html#K10" title="RINGCAT1:func.10">Morphs</a> <font color="Olive" title="b1">V</font>  st  <a href="ringcat1.html#K11" title="RINGCAT1:func.11">dom</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K12" title="RINGCAT1:func.12">cod</a> <font color="Olive" title="b3">f</font> holds <br/> ex <font color="Olive" title="b4">G1</font>, <font color="Olive" title="b5">G2</font>, <font color="Olive" title="b6">G3</font> being    <a href="ringcat1.html#M2" title="RINGCAT1:mode.2">Element</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b4">G1</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b5">G2</font> &amp; <font color="Olive" title="b5">G2</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b6">G3</font> &amp; <font color="Olive" title="b2">g</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b5">G2</font>,<font color="Olive" title="b6">G3</font> &amp; <font color="Olive" title="b3">f</font> is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b4">G1</font>,<font color="Olive" title="b5">G2</font> )</div></div>
