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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/>

<b>assume </b><a NAME="E1:25"/><i><font color="Green">E23</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:25"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E3:25"/><b>then </b><i><font color="Green">E24</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E4:25"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="irrat_1.html#E1:25"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b> <a href="rvsum_1.html#K15">Sum</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T32">FINSEQ_5:32</a></i>
<br/>.= 
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="irrat_1.html#E3:25"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T106">RVSUM_1:106</a></i>
;<br/><br/>


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