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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: RING_5:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font> holds   <a href="ring_5.html#NK1" title="RING_5:NK.1">card</a> <span class="p1">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ring_5.html#NK1" title="RING_5:NK.1">card</a> <span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <font color="Olive" title="b2">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="ring_5.html#NK1" title="RING_5:NK.1">card</a> <span class="p2">(<span class="default"><a href="uproots.html#K7" title="UPROOTS:func.7">BRoots</a> <font color="Olive" title="b3">q</font></span>)</span></span>)</span></div></div>
