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<div>:: <span class="kw">deftheorem </span>   defines <a href="realalg1.html#K10" title="REALALG1:func.10">LowPositives(Poly)</a> <a onclick="hs(this)" href="javascript:()">REALALG1:def 25 : <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> holds   <a href="realalg1.html#K10" title="REALALG1:func.10">LowPositives(Poly)</a> <font color="Olive" title="b2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">p</font> where <font color="Olive" title="b3">p</font> is   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Olive" title="b1">R</font> : <font color="Olive" title="b3">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p1">(<span class="default"><a href="nat_1.html#K3" title="NAT_1:func.3">min*</a> <span class="p2"> { <span class="default"> <font color="Olive" title="b4">i</font> where <font color="Olive" title="b4">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : <font color="Olive" title="b3">p</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> </span> } </span> </span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">P</font> </span> } </span> ;<br/></span></div>
