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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E56">x1a</font></span>: <a NAME="T64"><span class="comment"><font color="firebrick">:: REALALG2:64</font></span><br/></a><div class="add"> 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  <font color="Olive">b<sub>2</sub></font> <a href="realalg2.html#V5" title="REALALG2:attr.5">-ordered</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> holds <br/> (  not <font color="Olive" title="b3">a</font> is <font color="Olive" title="b2">P</font> <a href="realalg2.html#V7" title="REALALG2:attr.7">-negative</a>  iff  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">a</font> )</div></div>
