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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: REALALG1:30</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> holds   <a href="realalg1.html#K4" title="REALALG1:func.4">OrdRel</a> <font color="Olive" title="b2">P</font> is   <a href="realalg1.html#NM3" title="REALALG1:NM.3">OrderRelation</a> of <font color="Olive" title="b1">R</font> ;<br/></div></div>
