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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<a NAME="E1:33"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font>, <a href="rfinseq2.html#K6" target="_self">sort_a</a> <font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="ref" href="rfinseq2.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E2:33"/><i><font color="Green">E22</font></i>: 
 <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> is <a href="integra2.html#V1">non-decreasing</a>
 
<b>by </b><i><a class="ref" href="rfinseq2.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E3:33"/>
 <a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font>, <a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="ref" href="rfinseq2.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E4:33"/><b>then </b>
 <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>, <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="ref" href="rfinseq2.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E5:33"/><b>then </b>
 <a href="rfinseq2.html#K6" target="_self">sort_a</a> <font color="Maroon">c<sub>1</sub></font>, <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:33"><i><font color="Green">E21</font></i></a>, <a class="ref" href="rfinseq.html#T2">RFINSEQ:2</a></i>;<br/>
<a NAME="E6:33"/><b>then </b>
 <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rfinseq2.html#K6" target="_self">sort_a</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E2:33"><i><font color="Green">E22</font></i></a>, <a class="ref" href="rfinseq2.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E7:33"/>
 <a href="rfinseq2.html#K5" target="_self">sort_d</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K6" target="_self">sort_a</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>


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