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<b>let </b><font color="Maroon" title="c1">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:()"><i><font color="Red">::  thesis: </font></i></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="c1">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="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="b1">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a> )</span><br/>

<a NAME="E1:22"/>
<font color="Maroon" title="c1">t</font> is    <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>by </b><i><a class="ref" href="finseq_3.html#T126" title="FINSEQ_3:th.126">FINSEQ_3:126</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c2">u</font> being  <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a>  <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="E3:22"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">u</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="ref" href="rfinseq.html#T35" title="RFINSEQ:th.35">RFINSEQ:35</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">u</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">u</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon" title="c2">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="c2">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a> )</span><br/>

<b>thus </b><a NAME="E4:22"/>
<font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">u</font> <a href="rfinseq.html#R1" title="RFINSEQ:pred.1">are_fiberwise_equipotent</a> 
 <b>by </b><i><a class="txt" href="scmbsort.html#E3:22"><i><font color="Green" title="E22">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">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="c2">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a> )</span><br/>

<a NAME="E5:22"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">u</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E3:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="rfinseq.html#T1" title="RFINSEQ:th.1">RFINSEQ:1</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon" title="c2">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> 
 <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a></span><br/>

<b>thus </b><a NAME="E7:22"/>
<font color="Maroon" title="c2">u</font> is <a href="seqm_3.html#V4" title="SEQM_3:attr.4">non-increasing</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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