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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th2</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: RINGCAT1:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">g</font>, <font color="Olive" title="b2">f</font> being   <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a>  st  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Olive" title="b2">f</font> holds <br/> ex <font color="Olive" title="b3">G1</font>, <font color="Olive" title="b4">G2</font>, <font color="Olive" title="b5">G3</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> st <br/>( <font color="Olive" title="b3">G1</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b4">G2</font> &amp; <font color="Olive" title="b4">G2</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Olive" title="b5">G3</font> &amp;  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(#  the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Olive" title="b1">g</font>, the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Olive" title="b1">g</font>, the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Olive" title="b1">g</font> #) is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b4">G2</font>,<font color="Olive" title="b5">G3</font> &amp;  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(#  the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Olive" title="b2">f</font>, the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Olive" title="b2">f</font>, the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Olive" title="b2">f</font> #) is    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Olive" title="b3">G1</font>,<font color="Olive" title="b4">G2</font> )</div></div>
