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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><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="E1:70"/><i><font color="Green">E30</font></i>: 
(  <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>2</sub></font> &amp;  <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>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:70"/><b>then </b><i><font color="Green">E31</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>2</sub></font> &amp;  <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="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>;<br/>
<a NAME="E3:70"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K11" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K11" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrixr1.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E4:70"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K11" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="matrixr1.html#K12" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#T52" target="_self">Th52</a>, <a class="txt" href="matrixr1.html#E1:70"><i><font color="Green">E30</font></i></a></i>;<br/>
<a NAME="E5:70"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</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="euclid_2.html#T8">EUCLID_2:8</a></i>;<br/>
<a NAME="E6:70"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrixr1.html#K12" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrixr1.html#K11" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrixr1.html#T53" target="_self">Th53</a>, <a class="txt" href="matrixr1.html#E2:70"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:70"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</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="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="rvsum_1.html#K9">*</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#E4:70"><i><font color="Green">E33</font></i></a>, <a class="txt" href="matrixr1.html#E3:70"><i><font color="Green">E32</font></i></a>, <a class="ref" href="matrix_2.html#T15">MATRIX_2:15</a>, <a class="txt" href="matrixr1.html#E1:70"><i><font color="Green">E30</font></i></a></i>;<br/>


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