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<b>let </b><font color="Maroon" title="c1">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="c2">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="E1:60"/><i><font color="Green" title="E23">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">A</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">A</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="c2">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="c1">x</font> or  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </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="c1">x</font> ) )
 ;<br/>

<a NAME="E2:60"/><b>then </b><i><font color="Green" title="E24">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T12" title="MATRIX_2:th.12">MATRIX_2:12</a></i>;<br/>
<a NAME="E3:60"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">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="c1">x</font>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="matrix_2.html#T12" title="MATRIX_2:th.12">MATRIX_2:12</a></i>;<br/>
<a NAME="E4:60"/><i><font color="Green" title="E26">A4</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">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="c1">x</font>
 
<b>by </b><i><a class="ref" href="matrixr1.html#D10" target="_self" title="MATRIXR1:def.10">Def10</a></i>;<br/>
<a NAME="E5:60"/><b>then </b><i><font color="Green" title="E27">A5</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">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">A</font>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="matrix_2.html#T12" title="MATRIX_2:th.12">MATRIX_2:12</a></i>;<br/>
<a NAME="E6:60"/><i><font color="Green" title="E28">A6</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#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">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#D10" target="_self" title="MATRIXR1:def.10">Def10</a></i>;<br/>
<a NAME="E7:60"/><i><font color="Green" title="E29">A7</font></i>: 
 <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="c1">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#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="matrixr1.html#E2:60"><i><font color="Green" title="E24">A2</font></i></a></i>;<br/>
<a NAME="E8:60"/>
 <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="c1">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="c1">x</font>
 
<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#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="matrixr1.html#E2:60"><i><font color="Green" title="E24">A2</font></i></a></i>;<br/>
<a NAME="E9:60"/><b>then </b><i><font color="Green" title="E30">A8</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <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="c1">x</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">x</font></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#E2:60"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>
<a NAME="E10:60"/><i><font color="Green" title="E31">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">A</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> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></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#E5:60"><i><font color="Green" title="E27">A5</font></i></a></i>;<br/>
<a NAME="E11:60"/><i><font color="Green" title="E32">A10</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">A</font>
 
<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#E5:60"><i><font color="Green" title="E27">A5</font></i></a></i>;<br/>
<a NAME="E12:60"/><i><font color="Green" title="E33">A11</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <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="c1">x</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr1.html#E7:60"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a>, <a class="txt" href="matrixr1.html#E9:60"><i><font color="Green" title="E30">A8</font></i></a></i>;<br/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">A</font></span>)</span>,1 = 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">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" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_2.html#T15" title="MATRIX_2:th.15">MATRIX_2:15</a>, <a class="txt" href="matrixr1.html#E10:60"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="matrixr1.html#E6:60"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="matrixr1.html#E11:60"><i><font color="Green" title="E32">A10</font></i></a>, <a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span></span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_3.html#T24" title="MATRIX_3:th.24">MATRIX_3:24</a>, <a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="matrixr1.html#E4:60"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="matrixr1.html#E3:60"><i><font color="Green" title="E25">A3</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <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="c1">x</font></span>)</span></span>)</span> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span>,1
<b>by </b><i><a class="ref" href="matrixr1.html#T49" target="_self" title="MATRIXR1:th.49">Th49</a>, <a class="txt" href="matrixr1.html#E1:60"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="matrixr1.html#E3:60"><i><font color="Green" title="E25">A3</font></i></a></i>
<br/>.= 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <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="c1">x</font></span>)</span></span>)</span>,1
<b>by </b><i><a class="ref" href="matrix_2.html#T17" title="MATRIX_2:th.17">MATRIX_2:17</a>, <a class="txt" href="matrixr1.html#E12:60"><i><font color="Green" title="E33">A11</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E14:60"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrix_1.html#K4" title="MATRIX_1:func.4">@</a> </span>)</span> <a href="matrixr1.html#K11" title="MATRIXR1:func.11">*</a> <font color="Maroon" title="c1">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">x</font> <a href="matrixr1.html#K12" title="MATRIXR1:func.12">*</a> <font color="Maroon" title="c2">A</font>
 ;<br/>


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