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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">Th12</font></span>: <a NAME="T35"><span class="comment"><font color="firebrick">:: FIELD_11:35</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="ring_4.html#V3" title="RING_4:attr.3">constant</a>   <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span><br/>  for <font color="Olive" title="b3">m</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b3">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="field_11.html#K5" title="FIELD_11:func.5">nonConstantPolys</a> <font color="Olive" title="b1">F</font></span>)</span> holds <br/> <a href="field_11.html#K7" title="FIELD_11:func.7">Poly</a> (<font color="Olive" title="b3">m</font>,<span class="p1">(<span class="default"><a href="field_1.html#NK3" title="FIELD_1:NK.3">anpoly</a> (<span class="p2">(<span class="default"><a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b2">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Olive" title="b2">p</font></span>)</span>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="field_11.html#NK6" title="FIELD_11:NK.6">LM</a> <span class="p1">(<span class="default"><a href="field_11.html#K7" title="FIELD_11:func.7">Poly</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b2">p</font>)</span>)</span></div></div>
