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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">lemP</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: REALALG3:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <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 <br/> ( <font color="Olive" title="b2">P</font> <a href="ideal_1.html#K12" title="IDEAL_1:func.12">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="realalg3.html#K4" title="REALALG3:func.4">^+</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font> <a href="realalg3.html#K4" title="REALALG3:func.4">^+</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="realalg3.html#K4" title="REALALG3:func.4">^+</a></span>)</span> <a href="ideal_1.html#K12" title="IDEAL_1:func.12">+</a> <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">P</font> <a href="realalg3.html#K4" title="REALALG3:func.4">^+</a>  )</div></div>
