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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th10</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: FIELD_4:15</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">S</font> being   <a href="field_4.html#NM1" title="FIELD_4:NM.1">RingExtension</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">p1</font>, <font color="Olive" title="b6">q1</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b3">p</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">p1</font> &amp; <font color="Olive" title="b4">q</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b6">q1</font> holds <br/><font color="Olive" title="b3">p</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Olive" title="b4">q</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">p1</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Olive" title="b6">q1</font></div></div>
