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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E59">av00</font></span>: <a NAME="T67"><span class="comment"><font color="firebrick">:: REALALG2:67</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><br/>  for <font color="Olive" title="b3">a</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/> (  not <font color="Olive" title="b3">a</font> is <font color="Olive" title="b2">P</font> <a href="realalg2.html#V5" title="REALALG2:attr.5">-ordered</a>  iff  <a href="realalg2.html#NK4" title="REALALG2:NK.4">abs</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">R</font></span>)</span> )</div></div>
