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<span class="kw">let </span><font color="Maroon" title="c40">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c40">t</font>,<font color="Olive" title="b1">u</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  &amp; <font color="Olive" title="b1">u</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c40">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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Olive" title="b1">u</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c41">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> <span class="kw"> such that </span><br/><a NAME="E2:40"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
<font color="Maroon" title="c40">t</font>,<font color="Maroon" title="c41">u</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 <span class="kw">and </span><br/><a NAME="E3:40"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c41">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> 
 <span class="kw">and </span><br/><a NAME="E4:40"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
<font color="Maroon" title="c41">u</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#T33" title="RFINSEQ:th.33">RFINSEQ:33</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c42">u</font> = <font color="Maroon" title="c41">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40"><span class="lab"><font color="Green" title="E58">A2</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c43">p</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c40">t</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c44">q</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c42">u</font>;<br/>
<a NAME="E6:40"/>
<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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c40">t</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c42">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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E4:40"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="ref" href="scmbsort.html#D3" target="_self" title="SCMBSORT:def.3">Def3</a></span>;<br/>
<a NAME="E7:40"/><span class="kw">then </span>
<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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c40">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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c42">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T1" title="FUNCT_1:th.1">FUNCT_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:40"/>
 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="c40">t</font>,<font color="Olive" title="b1">u</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  &amp; <font color="Olive" title="b1">u</font> is  <a href="valued_0.html#V10" title="VALUED_0:attr.10">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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c40">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#K5" title="SCMFSA_2:func.5">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Olive" title="b1">u</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E4:40"><span class="lab"><font color="Green" title="E59">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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