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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">XYZb</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: REALALG3:24</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   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">E</font>  st <font color="Olive" title="b3">a</font> <a href="o_ring_1.html#K1" title="O_RING_1:func.1">^2</a>  <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">F</font> holds <br/> for <font color="Olive" title="b4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Olive" title="b1">F</font>,<span class="p2"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b3">a</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</span>)</span>  ex <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">c2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Olive" title="b1">F</font>,<span class="p2"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b3">a</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</span>)</span> st <br/>( <font color="Olive" title="b5">c1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">F</font> &amp; <font color="Olive" title="b6">c2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">F</font> &amp; <font color="Olive" title="b4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">c1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realalg3.html#K3" title="REALALG3:func.3">@</a> (<span class="p3">(<span class="default"><a href="field_6.html#K6" title="FIELD_6:func.6">FAdj</a> (<font color="Olive" title="b1">F</font>,<span class="p4"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b3">a</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span>)</span>)</span>,<font color="Olive" title="b3">a</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b6">c2</font></span>)</span> )</div></div>
