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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E25</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; (  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> ) )
 ;<br/>

<a NAME="E2:62"/><i><font color="Green">E26</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E3:62"/><i><font color="Green">E27</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>;<br/>
<a NAME="E4:62"/><i><font color="Green">E28</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E5:62"/><i><font color="Green">E29</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a>, <a class="txt" href="matrixr1.html#E4:62"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E6:62"/><i><font color="Green">E30</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="matrixr1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E7:62"/><i><font color="Green">E31</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="matrixr1.html#D9" target="_self">Def9</a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="txt" href="matrixr1.html#E2:62"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E8:62"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#D9" target="_self">Def9</a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="txt" href="matrixr1.html#E2:62"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E9:62"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_3.html#D4">MATRIX_3:def 4</a>, <a class="txt" href="matrixr1.html#E2:62"><i><font color="Green">E26</font></i></a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E10:62"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_3.html#D4">MATRIX_3:def 4</a>, <a class="txt" href="matrixr1.html#E5:62"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E11:62"/><i><font color="Green">E34</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="matrix_3.html#D4">MATRIX_3:def 4</a>, <a class="txt" href="matrixr1.html#E5:62"><i><font color="Green">E29</font></i></a></i>;<br/>
<a NAME="E12:62"/><i><font color="Green">E35</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E7:62"><i><font color="Green">E31</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="txt" href="matrixr1.html#E9:62"><i><font color="Green">E32</font></i></a></i>;<br/>
 <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,1 = 
 <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_2.html#T15">MATRIX_2:15</a>, <a class="txt" href="matrixr1.html#E10:62"><i><font color="Green">E33</font></i></a>, <a class="txt" href="matrixr1.html#E6:62"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrixr1.html#E11:62"><i><font color="Green">E34</font></i></a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_3.html#T24">MATRIX_3:24</a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="txt" href="matrixr1.html#E4:62"><i><font color="Green">E28</font></i></a>, <a class="txt" href="matrixr1.html#E3:62"><i><font color="Green">E27</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrixr1.html#T49" target="_self">Th49</a>, <a class="txt" href="matrixr1.html#E1:62"><i><font color="Green">E25</font></i></a>, <a class="txt" href="matrixr1.html#E3:62"><i><font color="Green">E27</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K9" target="_self">ColVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_2.html#T17">MATRIX_2:17</a>, <a class="txt" href="matrixr1.html#E12:62"><i><font color="Green">E35</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E14:62"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K11" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="matrixr1.html#K12" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div>
