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

<b>thus </b><a NAME="E1:1_1_2"/>
for <font color="Olive">p1</font>, <font color="Olive">p2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a>   st  <a href="finseq_1.html#K3">len</a> <font color="Olive">p1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font></span>)</span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <font color="Olive">p1</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font> ) &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">p2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font></span>)</span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <font color="Olive">p2</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font> ) holds <br/><font color="Olive">p1</font> <a href="hidden.html#R1">=</a> <font color="Olive">p2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> , <font color="Maroon">p2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:1_1_2_1"/><i><font color="Green">E41</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font></span>)</span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font> ) &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font></span>)</span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font> ) )
 ;<br/>

<a NAME="E2:1_1_2_1"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font> holds <br/><font color="Maroon">p1</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="matrix_5.html#K9">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:1_1_2_1_1"/><i><font color="Green">E42</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font> )
 ;<br/>

<a NAME="E2:1_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">i</font></span>)</span> <a href="complex1.html#K15">*'</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">i</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:1_1_2_1_1"/>
<font color="Maroon">p1</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="matrix_5.html#K9">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:1_1_2_1"/>
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>


</div>
