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<div><span class="kw">theorem </span><a NAME="T58"><span class="comment"><font color="firebrick">:: REALALG2:58</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_2.html#NM2" title="VECTSP_2:NM.2">domRing</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>, <font color="Olive" title="b5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font>  st <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> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> <a href="realalg2.html#R1" title="REALALG2:pred.1">&lt;</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b5">c</font> holds <br/><font color="Olive" title="b3">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b5">c</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> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b5">c</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T47" target="_self" onmouseover="rs('realalg2/T47')" onmouseout="rh()">c5</a>, <a class="ref" href="gcd_1.html#T1" onmouseover="rs('gcd_1/T1')" onmouseout="rh()">GCD_1:1</a></span>;<br/></div></div>
