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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E51">defppp</font></span>   defines <a href="realalg2.html#V5" title="REALALG2:attr.5">-ordered</a> <a onclick="hs(this)" href="javascript:()">REALALG2:def 7 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="realalg1.html#V13" title="REALALG1:attr.13">preordered</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</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">R</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="b1">R</font> holds <br/> ( <font color="Olive" title="b3">a</font> is <font color="Olive" title="b2">P</font> <a href="realalg2.html#V5" title="REALALG2:attr.5">-ordered</a>  iff <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="realalg1.html#K1" title="REALALG1:func.1">-</a> <font color="Olive" title="b2">P</font></span>)</span> );<br/></span></div>
