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<b>thus </b><a NAME="E1:21_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="rfinseq.html#V1">non-increasing</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="rfinseq.html#V1">non-increasing</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:21_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  )
 ;<br/>

<a NAME="E2:21_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="ref" href="rfinseq.html#T2">RFINSEQ:2</a></i>;<br/>
<b>hence </b><a NAME="E3:21_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="rfinseq.html#T36">RFINSEQ:36</a></i>;<br/>


</div><b>end;</b></div>


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