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<b>set </b><font color="Maroon">F</font> =  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> ;<br/>
<a NAME="E1:21"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="numbers.html#K6">ExtREAL</a>  st <br/>(  <a href="convfun1.html#K5" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="supinf_2.html#K13">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> </span>)</span></span>)</span> &amp; <font color="Olive">f</font> <a href="supinf_2.html#K13">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  &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="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> </span>)</span> holds <br/><font color="Olive">f</font> <a href="supinf_2.html#K13">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="supinf_2.html#K13">.</a> <font color="Olive">i</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> </span>)</span> <a href="supinf_2.html#K13">.</a> <span class="p2">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:21"/>
 <a href="convfun1.html#K5" target="_self">Sum</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K6">ExtREAL</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>


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