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<div><span class="kw">theorem </span><a NAME="T38"><span class="comment"><font color="firebrick">:: REALALG3:38</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">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">P</font> being   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <font color="Olive" title="b1">F</font> holds <br/> ( <font color="Olive" title="b3">P</font> <a href="realalg3.html#R1" title="REALALG3:pred.1">extends_to</a> <font color="Olive" title="b2">E</font> iff  for <font color="Olive" title="b4">f</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <font color="Olive">b<sub>3</sub></font> <a href="realalg3.html#V2" title="REALALG3:attr.2">-quadratic</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b2">E</font>  st  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">E</font> holds <br/><font color="Olive" title="b4">f</font> is  <a href="realalg2.html#V3" title="REALALG2:attr.3">trivial</a>  )</div></div>
