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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">lemPP</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: REALALG3:8</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">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">E</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>  st <font color="Olive" title="b3">E</font> <a href="field_7.html#R1" title="FIELD_7:pred.1">==</a> <font color="Olive" title="b1">F</font> holds <br/>( <font color="Olive" title="b3">E</font> is  <a href="realalg1.html#V14" title="REALALG1:attr.14">ordered</a>  &amp;  ex <font color="Olive" title="b4">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b3">E</font> st <br/>( <font color="Olive" title="b4">Q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b4">Q</font> is  <a href="realalg1.html#V12" title="REALALG1:attr.12">positive_cone</a>  ) )</div></div>
