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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<a NAME="E1:33"/>
 <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font>, <a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq2.html#D5" target="_self" title="RFINSEQ2:def.5">Def5</a></span>;<br/>
<a NAME="E2:33"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span>, <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq2.html#T27" target="_self" title="RFINSEQ2:th.27">Th27</a></span>;<br/>
<a NAME="E3:33"/>
 <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> is  <a href="integra2.html#V1" title="INTEGRA2:attr.1">non-decreasing</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq2.html#T24" target="_self" title="RFINSEQ2:th.24">Th24</a></span>;<br/>
<a NAME="E4:33"/><span class="kw">then </span>
 <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <font color="Maroon" title="c1">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="rfinseq2.html#D6" target="_self" title="RFINSEQ2:def.6">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:33"/>
 <a href="rfinseq2.html#K5" title="RFINSEQ2:func.5">sort_d</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <font color="Maroon" title="c1">f</font></span>)</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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