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<b>let </b><font color="Maroon">c<sub>39</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>40</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E2:56"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>39</sub></font>,<font color="Maroon">c<sub>40</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">c<sub>40</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  &amp; <font color="Maroon">c<sub>40</sub></font> is <a href="rfinseq.html#V1">non-increasing</a> )
 <b>by </b><i><a class="ref" href="scmbsort.html#T39" target="_self">Th39</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>41</sub></font> = <font color="Maroon">c<sub>40</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  <b>by </b><i><a class="txt" href="scmbsort.html#E2:56"><i><font color="Green">E56</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>42</sub></font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>39</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>43</sub></font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>41</sub></font>;<br/>
<a NAME="E4:56"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>39</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>41</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="scmbsort.html#K4" target="_self">Sorting-Function</a> 
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:56"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmbsort.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:56"/><b>then </b>
<a href="scmbsort.html#K4" target="_self">Sorting-Function</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>41</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T8">FUNCT_1:8</a></i>;<br/>
<b>hence </b><a NAME="E6:56"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <br/>( <font color="Maroon">c<sub>39</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Olive">b<sub>1</sub></font> is <a href="rfinseq.html#V1">non-increasing</a> &amp; <font color="Olive">b<sub>1</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  &amp; <a href="scmbsort.html#K4" target="_self">Sorting-Function</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" target="_self">.--&gt;</a> <font color="Maroon">c<sub>39</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6">fsloc</a> 0</span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="scmbsort.html#E2:56"><i><font color="Green">E56</font></i></a></i>;<br/>


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