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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: REALALG3:44</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">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="b4">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="b5">b</font>, <font color="Olive" title="b6">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b3">E</font>  st <font color="Olive" title="b5">b</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a</font> &amp; <font color="Olive" title="b6">c</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">a</font> &amp;  not <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">b</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>) 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="b6">c</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</div></div>
