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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E67">multi2</font></span>: <a NAME="T67"><span class="comment"><font color="firebrick">:: FIELD_14:67</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">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><br/>  for <font color="Olive" title="b3">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="uproots.html#K6" title="UPROOTS:func.6">multiplicity</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">a</font>) iff ( <span class="p1">(<span class="default"><a href="field_9.html#K2" title="FIELD_9:func.2">X-</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="polynom5.html#K3" title="POLYNOM5:func.3">`^</a> <font color="Olive" title="b4">n</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b2">p</font> &amp;  not <span class="p1">(<span class="default"><a href="field_9.html#K2" title="FIELD_9:func.2">X-</a> <font color="Olive" title="b3">a</font></span>)</span> <a href="polynom5.html#K3" title="POLYNOM5:func.3">`^</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b2">p</font> ) )</div></div>
