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<b>let </b><font color="Maroon" title="c39">t</font> be    <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> ;<br/>

<b>consider </b><font color="Maroon" title="c40">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> <b> such that </b><br/><a NAME="E2:47"/><i><font color="Green" title="E45">A1</font></i>: 
( <font color="Maroon" title="c39">t</font>,<font color="Maroon" title="c40">u</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon" title="c40">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="Maroon" title="c40">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a> )
 <b>by </b><i><a class="ref" href="scmbsort.html#T39" target="_self" title="SCMBSORT:th.39">Th39</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c41">u</font> = <font color="Maroon" title="c40">u</font> as    <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>  <b>by </b><i><a class="txt" href="scmbsort.html#E2:47"><i><font color="Green" title="E45">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c42">p</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">t</font>;<br/>
<b>set </b><font color="Maroon" title="c43">q</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c41">u</font>;<br/>
<a NAME="E4:47"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">t</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c41">u</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="scmbsort.html#K4" title="SCMBSORT:func.4">Sorting-Function</a> 
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:47"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="scmbsort.html#D3" target="_self" title="SCMBSORT:def.3">Def3</a></i>;<br/>
<a NAME="E5:47"/><b>then </b>
<a href="scmbsort.html#K4" title="SCMBSORT:func.4">Sorting-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c41">u</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/>
<b>hence </b><a NAME="E6:47"/>
 ex <font color="Olive" title="b1">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="Maroon" title="c39">t</font>,<font color="Olive" title="b1">u</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Olive" title="b1">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a> &amp; <font color="Olive" title="b1">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; <a href="scmbsort.html#K4" title="SCMBSORT:func.4">Sorting-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c39">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <font color="Olive" title="b1">u</font> )
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:47"><i><font color="Green" title="E45">A1</font></i></a></i>;<br/>


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