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<b>let </b><font color="Maroon">c<sub>39</sub></font>, <font color="Maroon">c<sub>40</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="ami_1.html#K14">FinPartSt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> , <a href="ami_1.html#K14">FinPartSt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:54_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>39</sub></font> iff ex <font color="Olive">b<sub>3</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ex <font color="Olive">b<sub>4</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <br/>( <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Olive">b<sub>4</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  &amp; <font color="Olive">b<sub>4</sub></font> is <a href="rfinseq.html#V1">non-increasing</a> &amp; <font color="Olive">b<sub>1</sub></font> <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="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <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>4</sub></font> ) )
 <b>and </b><br/><a NAME="E2:54_1_2"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>40</sub></font> iff ex <font color="Olive">b<sub>3</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ex <font color="Olive">b<sub>4</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <br/>( <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Olive">b<sub>4</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  &amp; <font color="Olive">b<sub>4</sub></font> is <a href="rfinseq.html#V1">non-increasing</a> &amp; <font color="Olive">b<sub>1</sub></font> <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="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <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>4</sub></font> ) )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ex <font color="Olive">b<sub>2</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <br/>( <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Olive">b<sub>2</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a>  &amp; <font color="Olive">b<sub>2</sub></font> is <a href="rfinseq.html#V1">non-increasing</a> &amp; <font color="Maroon">a<sub>1</sub></font> <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="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <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>2</sub></font> );<br/>
<a NAME="E3:54_1_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>39</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:54_1_2"><i><font color="Green">E53</font></i></a></i>;<br/>
<a NAME="E4:54_1_2"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>40</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 
<b>by </b><i><a class="txt" href="scmbsort.html#E2:54_1_2"><i><font color="Green">E54</font></i></a></i>;<br/>
<b>thus </b><a NAME="E5:54_1_2"/>
<font color="Maroon">c<sub>39</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>40</sub></font>
 <b>from </b><i><a class="ref" href="ami_3.html#S2">AMI_3:sch 2</a>(<a class="txt" href="scmbsort.html#E3:54_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmbsort.html#E4:54_1_2"><i><font color="Green">E56</font></i></a>);</i><br/>


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