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<div>:: <span class="kw">deftheorem </span>   defines <a href="realalg3.html#R1" title="REALALG3:pred.1">extends_to</a> <a onclick="hs(this)" href="javascript:()">REALALG3:def 7 : <br/></a><span> 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">E</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">P</font> being   <a href="realalg1.html#NM2" title="REALALG1:NM.2">Ordering</a> of <font color="Olive" title="b1">F</font> holds <br/> ( <font color="Olive" title="b3">P</font> <a href="realalg3.html#R1" title="REALALG3:pred.1">extends_to</a> <font color="Olive" title="b2">E</font> iff  ex <font color="Olive" title="b4">O</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">E</font> st <br/>( <font color="Olive" title="b3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">O</font> &amp; <font color="Olive" title="b4">O</font> is  <a href="realalg1.html#V12" title="REALALG1:attr.12">positive_cone</a>  ) );<br/></span></div>
