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<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E28">A1</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">A</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:67"/><b>then </b><i><font color="Green" title="E29">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#D9" target="_self" title="MATRIXR1:def.9">Def9</a></i>;<br/>
<a NAME="E3:67"/>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="matrixr1.html#D9" target="_self" title="MATRIXR1:def.9">Def9</a>, <a class="txt" href="matrixr1.html#E1:67"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/>
<a NAME="E4:67"/><b>then </b><i><font color="Green" title="E30">A3</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a>, <a class="txt" href="matrixr1.html#E2:67"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="matrixr1.html#E1:67"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K11" title="MATRIXR1:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c2">x</font></span>)</span> = 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="matrixr1.html#T47" target="_self" title="MATRIXR1:th.47">Th47</a>, <a class="txt" href="matrixr1.html#E1:67"><i><font color="Green" title="E28">A1</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c2">x</font></span>)</span></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="matrixr1.html#T40" target="_self" title="MATRIXR1:th.40">Th40</a>, <a class="txt" href="matrixr1.html#E1:67"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="matrixr1.html#E2:67"><i><font color="Green" title="E29">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K11" title="MATRIXR1:func.11">*</a> <font color="Maroon" title="c2">x</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#T56" target="_self" title="MATRIXR1:th.56">Th56</a>, <a class="txt" href="matrixr1.html#E4:67"><i><font color="Green" title="E30">A3</font></i></a></i>
;<br/>


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