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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E15">Def7</font></span>   defines <a href="scmfsa_m.html#K10" title="SCMFSA_M:func.10">Sorting-Function</a> <a onclick="hs(this)" href="javascript:()">SCMFSA_M:def 7 : <br/></a><span> for <font color="Olive">b<sub>1</sub></font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="memstr_0.html#K11" title="MEMSTR_0:func.11">FinPartSt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K11" title="MEMSTR_0:func.11">FinPartSt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span> holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_m.html#K10" title="SCMFSA_M:func.10">Sorting-Function</a>  iff  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> iff  ex <font color="Olive" title="b4">t</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b5">u</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>( <font color="Olive" title="b4">t</font>,<font color="Olive" title="b5">u</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  &amp; <font color="Olive" title="b5">u</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Olive" title="b5">u</font> is  <a href="valued_0.html#V8" title="VALUED_0:attr.8">non-increasing</a>  &amp; <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Olive" title="b5">u</font> ) ) );<br/></span></div>
