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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: MODCAT_1:8</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>  st  <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modcat_1.html#K6" title="MODCAT_1:func.6">cod'</a> <font color="Olive" title="b4">f</font> holds <br/> ex <font color="Olive" title="b5">G1</font>, <font color="Olive" title="b6">G2</font>, <font color="Olive" title="b7">G3</font> being   <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>   <a href="modcat_1.html#M2" title="MODCAT_1:mode.2">Element</a> of <font color="Olive" title="b2">V</font> st <br/>( <font color="Olive" title="b3">g</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Olive" title="b6">G2</font>,<font color="Olive" title="b7">G3</font> &amp; <font color="Olive" title="b4">f</font> is    <a href="mod_2.html#M1" title="MOD_2:mode.1">Morphism</a> of <font color="Olive" title="b5">G1</font>,<font color="Olive" title="b6">G2</font> )</div></div>
