<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">e1</font>, <font color="Maroon" title="c2">e2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> holds <br/><font color="Maroon" title="c1">e1</font> <a href="matrprob.html#NK7" title="MATRPROB:NK.7">"*"</a> <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Olive" title="b2">f2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> implies <font color="Maroon" title="c1">e1</font> <a href="matrprob.html#NK7" title="MATRPROB:NK.7">"*"</a> <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c4">f2</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:47"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">e2</font> &amp; <font color="Maroon" title="c1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">e1</font> <a href="matrprob.html#NK7" title="MATRPROB:NK.7">"*"</a> <font color="Maroon" title="c2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c4">f2</font></span><br/>

<span class="kw">hence </span><font color="Maroon" title="c1">e1</font> <a href="matrprob.html#NK7" title="MATRPROB:NK.7">"*"</a> <font color="Maroon" title="c2">e2</font> = 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrprob.html#T35" target="_self" title="MATRPROB:th.35">Th35</a>, <a class="ref" href="matrprob.html#T36" target="_self" title="MATRPROB:th.36">Th36</a></span>
<br/>.= 
<font color="Maroon" title="c3">f1</font> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <font color="Maroon" title="c4">f2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fvsum_1.html#D10" title="FVSUM_1:def.10">FVSUM_1:def 10</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
