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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th47</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: UPROOTS:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="vectsp_2.html#NM1" title="VECTSP_2:NM.1">comRing</a><br/>  for <font color="Olive" title="b2">r</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> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">r</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a> <font color="Olive" title="b3">p</font> holds <br/><font color="Olive" title="b3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="polynom5.html#K5" title="POLYNOM5:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">r</font></span>)</span>,<span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">L</font></span>)</span></span><a href="polynom5.html#K5" title="POLYNOM5:func.5">%&gt;</a></span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <span class="p1">(<span class="default"><a href="uproots.html#K5" title="UPROOTS:func.5">poly_quotient</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">r</font>)</span>)</span></div></div>
