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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: REALALG3:45</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="field_3.html#V3" title="FIELD_3:attr.3">polynomial_disjoint</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">a</font>, <font color="Olive" title="b4">b</font> being   non  <a href="realalg1.html#NV8" title="REALALG1:NV.8">square</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">F</font>  holds <br/>(  not <font color="Olive" title="b4">b</font> <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="b3">a</font> or <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"><span class="p2">(<span class="default"><a href="field_9.html#K16" title="FIELD_9:func.16">sqrt</a> <font color="Olive" title="b3">a</font></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>) or <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"><span class="p2">(<span class="default"><a href="field_9.html#K16" title="FIELD_9:func.16">sqrt</a> <font color="Olive" title="b4">b</font></span>)</span></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>) )</div></div>
