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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th15</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: ALGNUM_1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">B</font> being   <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><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">A</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">B</font>  st <font color="Olive" title="b1">A</font> is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Olive" title="b2">B</font> holds <br/> <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K1" title="POLYNOM4:func.1">Leading-Monomial</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b5">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<span class="p2">(<span class="default"><a href="polynom4.html#K1" title="POLYNOM4:func.1">Leading-Monomial</a> <font color="Olive" title="b3">p</font></span>)</span>,<font color="Olive" title="b5">x</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b5">x</font>)</span>)</span></div></div>
