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<b>let </b><font color="Maroon" title="c1">F</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> 1 )</span><br/>

<b>assume </b><a NAME="E1:57"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> 1</span><br/>

<a NAME="E2:57"/><b>then </b>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> 1</span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<b>hence </b><a NAME="E3:57"/>
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> 1
 <b>by </b><i><a class="ref" href="finsop_1.html#T12" title="FINSOP_1:th.12">FINSOP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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