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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: RINGCAT1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font>, <font color="Olive" title="b4">G4</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b5">f</font> being    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/>  for <font color="Olive" title="b6">g</font> being    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font><br/>  for <font color="Olive" title="b7">h</font> being    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b3">G3</font>,<font color="Olive" title="b4">G4</font>  st <font color="Olive" title="b1">G1</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b2">G2</font> &amp; <font color="Olive" title="b2">G2</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b3">G3</font> &amp; <font color="Olive" title="b3">G3</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b4">G4</font> holds <br/><font color="Olive" title="b7">h</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">g</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">h</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Olive" title="b6">g</font></span>)</span> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Olive" title="b5">f</font></div></div>
