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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: REALALG3:51</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">p</font> being   <a href="ring_2.html#V5" title="RING_2:attr.5">irreducible</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="b4">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="b5">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b4">E</font>  st  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Olive" title="b3">p</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  &amp; <font color="Olive" title="b5">a</font> <a href="field_4.html#R1" title="FIELD_4:pred.1">is_a_root_of</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">E</font> holds <br/><font color="Olive" title="b2">P</font> <a href="realalg3.html#R1" title="REALALG3:pred.1">extends_to</a>  <a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Olive" title="b1">F</font>,<span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b5">a</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</div></div>
