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



<b>assume </b><a NAME="E1:50"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 ;<br/>

<i><font color="Green">E48</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="matrixr1.html#K12">*</a> <font color="Maroon">M</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span>,1</span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D12">MATRIXR1:def 12</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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_1.html#D8">MATRIX_1:def 8</a></i>
;<br/>
<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:50_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="matrixr1.html#K12">*</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:50_2"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span>,1</span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="matrprob.html#T1" target="_self">Th1</a>, , <a class="ref" href="matrix_1.html#D8">MATRIX_1:def 8</a></i>;<br/><a NAME="E3:50_2"/><i><font color="Green">E51</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="matrixr1.html#D10">MATRIXR1:def 10</a></i>;<br/><a NAME="E4:50_2"/><b>then </b>
(  <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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> &amp;  <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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> )
 <b>by </b><i/>;<br/><a NAME="E5:50_2"/><b>then </b>
(  <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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp;  <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">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> )
 <b>by </b><i><a class="ref" href="matrixr1.html#T48">MATRIXR1:48</a></i>;<br/><a NAME="E6:50_2"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span></span>)</span> &amp; <font color="Maroon">i</font> <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"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="matrprob.html#T1" target="_self">Th1</a>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:50_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,<font color="Maroon">i</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i/>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span> <a href="matrixr1.html#K6">*</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_1.html#K3">*</a> 1,<font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K10">LineVec2Mx</a> <font color="Maroon">p</font></span>)</span>,1</span>)</span> <a href="matrprob.html#NK7" target="_self">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">M</font>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="txt" href="matrprob.html#E2:50"><i><font color="Green">E48</font></i></a>, </i>
<br/>.= 
<font color="Maroon">p</font> <a href="matrprob.html#NK7" target="_self">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">M</font>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#T48">MATRIXR1:48</a></i>
;<br/><b>hence </b><a NAME="E9:50_2"/>
<font color="Maroon">p</font> <a href="matrprob.html#NK7" target="_self">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">M</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="matrixr1.html#K12">*</a> <font color="Maroon">M</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="matrixr1.html#D12">MATRIXR1:def 12</a></i>;<br/></div>
<b>end;</b></div>


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