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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">div3</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: RING_4:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">r</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">u</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b5">p</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">F</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">r</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span> <a href="hurwitz.html#K6" title="HURWITZ:func.6">mod</a> <font color="Olive" title="b5">p</font></span>)</span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b4">u</font></span>)</span> <a href="hurwitz.html#K6" title="HURWITZ:func.6">mod</a> <font color="Olive" title="b5">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">r</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b3">q</font></span>)</span> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <font color="Olive" title="b4">u</font></span>)</span> <a href="hurwitz.html#K6" title="HURWITZ:func.6">mod</a> <font color="Olive" title="b5">p</font></div></div>
