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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">lem23</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: REALALG3:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="realalg1.html#V14" title="REALALG1:attr.14">ordered</a>  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">P</font> being   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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="b4">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>  st <font color="Olive" title="b4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b3">f</font> &amp; (  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font><br/>  for <font color="Olive" title="b6">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font>  st <font color="Olive" title="b6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> holds <br/>(  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b6">q</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  &amp;  <a href="ratfunc1.html#NK3" title="RATFUNC1:NK.3">LC</a> <font color="Olive" title="b6">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> ) ) holds <br/> <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Olive" title="b4">p</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </div></div>
