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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</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="E1:68"/><i><font color="Green">E29</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:68"/><i><font color="Green">E30</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="E3:68"/><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#K10" target="_self">LineVec2Mx</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> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E4:68"/><i><font color="Green">E32</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="E5:68"/><i><font color="Green">E33</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>2</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/>
<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>3</sub></font></span>)</span> = 
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>3</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#E2:68"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
 <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>2</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>3</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#E3:68"><i><font color="Green">E31</font></i></a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</font></i></a></i>
;<br/>
<i><font color="Green">E35</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>3</sub></font></span>)</span> = 
 <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#E2:68"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
 <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>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D10" target="_self">Def10</a>, <a class="txt" href="matrixr1.html#E5:68"><i><font color="Green">E33</font></i></a></i>
<br/>.= 
 <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>2</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>3</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#E1:68"><i><font color="Green">E29</font></i></a>, <a class="txt" href="matrixr1.html#E3:68"><i><font color="Green">E31</font></i></a></i>
;<br/>
<a NAME="E8:68"/><i><font color="Green">E36</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <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>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E4:68"><i><font color="Green">E32</font></i></a>, <a class="ref" href="matrix_3.html#D4">MATRIX_3:def 4</a>, <a class="txt" href="matrixr1.html#E2:68"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrixr1.html#K12" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> = 
 <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"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,1
<b>by </b><i><a class="ref" href="matrixr1.html#T50" target="_self">Th50</a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</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"><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>3</sub></font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K10" target="_self">LineVec2Mx</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrixr1.html#K6" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_4.html#T63">MATRIX_4:63</a>, <a class="txt" href="matrixr1.html#E1:68"><i><font color="Green">E29</font></i></a>, <a class="txt" href="matrixr1.html#E4:68"><i><font color="Green">E32</font></i></a>, <a class="txt" href="matrixr1.html#E5:68"><i><font color="Green">E33</font></i></a>, <a class="txt" href="matrixr1.html#E2:68"><i><font color="Green">E30</font></i></a>, <a class="txt" href="matrixr1.html#E3:68"><i><font color="Green">E31</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="matrixr1.html#K12" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="matrixr1.html#K12" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="matrixr1.html#E6:68"><i><font color="Green">E34</font></i></a>, <a class="ref" href="matrixr1.html#T55" target="_self">Th55</a>, <a class="txt" href="matrixr1.html#E8:68"><i><font color="Green">E36</font></i></a>, <a class="txt" href="matrixr1.html#E7:68"><i><font color="Green">E35</font></i></a></i>
;<br/>


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