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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: REALALG2:41</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> holds <br/> ( <font color="Olive" title="b1">F</font> is  <a href="realalg2.html#V2" title="REALALG2:attr.2">formally_real</a>  iff  for <font color="Olive" title="b2">f</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="realalg2.html#V4" title="REALALG2:attr.4">quadratic</a>  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b1">F</font>  st  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <font color="Olive" title="b2">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="b1">F</font> holds <br/><font color="Olive" title="b2">f</font> is  <a href="realalg2.html#V3" title="REALALG2:attr.3">trivial</a>  )</div></div>
