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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="convfun1.html#K4" target="_self">RLS_Real</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E34</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> holds <br/><font color="Maroon">a</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 ;<br/>

<a NAME="E3:28"/><i><font color="Green">E41</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">c</font> = <font color="Maroon">b</font>;<br/>
<b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">b</font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="supinf_1.html#K3">REAL</a>  ;<br/>
<a NAME="E5:28"/><i><font color="Green">E45</font></i>: 
 <a href="convfun1.html#K5" target="_self">Sum</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rvsum_1.html#K15">Sum</a> <font color="Maroon">c</font>
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E6:28"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">b</font> holds <br/><font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="seq_1.html#K2">.</a> <font color="Olive">i</font> ) )
 
;<br/>
<b>hence </b><a NAME="E7:28"/>
 <a href="convfun1.html#K5" target="_self">Sum</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">b</font>
 <b>by </b><i>, </i>;<br/>


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