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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E79">lembas2b</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: FIELD_6:63</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">E</font> being   <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">a</font> being  <font color="Olive">b<sub>1</sub></font> <a href="field_6.html#V2" title="FIELD_6:attr.2">-algebraic</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">E</font><br/>  for <font color="Olive" title="b4">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_6.html#K7" title="FIELD_6:func.7">Base</a> <font color="Olive" title="b3">a</font><br/>  for <font color="Olive" title="b5">p</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">F</font>  st  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b5">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <span class="p1">(<span class="default"><a href="field_6.html#NK9" title="FIELD_6:NK.9">MinPoly</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">F</font>)</span>)</span> &amp; (  for <font color="Olive" title="b6">i</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>   st <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <span class="p1">(<span class="default"><a href="field_6.html#NK9" title="FIELD_6:NK.9">MinPoly</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">F</font>)</span>)</span> holds <br/><font color="Olive" title="b5">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b6">i</font></span>)</span> ) holds <br/> <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Olive" title="b4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Olive" title="b5">p</font>,<font color="Olive" title="b3">a</font>)</div></div>
