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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">c10</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: REALALG2:53</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>, <font color="Olive" title="b4">b</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> <a href="realalg2.html#R1" title="REALALG2:pred.1">&lt;</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">b</font> iff  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">b</font> <a href="realalg2.html#R1" title="REALALG2:pred.1">&lt;</a> <font color="Olive" title="b2">P</font>, <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b3">a</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T42" target="_self" onmouseover="rs('realalg2/T42')" onmouseout="rh()">c10a</a>, <a class="ref" href="rlvect_1.html#T18" onmouseover="rs('rlvect_1/T18')" onmouseout="rh()">RLVECT_1:18</a></span>;<br/></div></div>
