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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">fi1</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: REALALG2:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="realalg1.html#V13" title="REALALG1:attr.13">preordered</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#NM1" title="REALALG1:NM.1">Preordering</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="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">F</font>  st  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">F</font> <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">a</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">F</font> <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">b</font> holds <br/>( <font color="Olive" title="b3">a</font> <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">b</font> iff <font color="Olive" title="b4">b</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">a</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  )</div></div>
