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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E55">Th52</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: UPROOTS:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="uproots.html#V1" title="UPROOTS:attr.1">non-zero</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">L</font> holds   <a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b2">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">x</font>)</span>)</span></div></div>
