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<div><span class="kw">theorem </span><a NAME="T77"><span class="comment"><font color="firebrick">:: REALALG2:77</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="realalg1.html#V13" title="REALALG1:attr.13">preordered</a>  <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">F</font><br/>  for <font color="Olive" title="b3">a</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <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">F</font><br/>  for <font color="Olive" title="b4">b</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">F</font> holds   <a href="realalg2.html#NK4" title="REALALG2:NK.4">abs</a> (<font color="Olive" title="b2">P</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a</font> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realalg2.html#NK4" title="REALALG2:NK.4">abs</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">b</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><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>)</span>)</span> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a></span>)</span></div></div>
