<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="matrix_1.html#NM4">Matrix</a> of <font color="Maroon">K</font>, <font color="Maroon">B</font> be   <a href="matrix_1.html#NM4">Matrix</a> of <font color="Maroon">K</font>;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green">E43</font></i>: 
(  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E3:30"/><i><font color="Green">E45</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D7">MATRIX_1:def 7</a></i>;<br/>
<a NAME="E4:30"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span>
 
<b>by </b><i>, , <a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>;<br/>
<a NAME="E5:30"/><b>then </b><i><font color="Green">E49</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span> )
 
<b>by </b><i/>;<br/>
<i><font color="Green">E50</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> = 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_1.html#D7">MATRIX_1:def 7</a></i>
<br/>.= 
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font>
<b>by </b><i>, </i>
;<br/>
<a NAME="E7:30"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, , </i>;<br/>
<b>then </b><i><font color="Green">E51</font></i>:  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font>
<b>by </b><i>, </i>
;<br/>
<i><font color="Green">E52</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D7">MATRIX_1:def 7</a></i>
;<br/>
<a NAME="E10:30"/><i><font color="Green">E59</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<div><i><font color="Green">E68</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:30_4"/><i><font color="Green">E69</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</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"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E2:30_4"/>
 <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:30_4"/><b>then </b><i><font color="Green">E75</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K3">dom</a> <span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setwop_2.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="matrix_1.html#D5">MATRIX_1:def 5</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_4_1"/>
(  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0 or  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_4_1_1"><b>suppose </b></a><a NAME="E1:30_4_1_1"/>
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_4_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="matrix_1.html#D4">MATRIX_1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_4_1_2"><b>suppose </b></a><a NAME="E1:30_4_1_2"/>
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:30_4_1_2"/><b>then </b>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</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">A</font>
 <b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>;<br/><a NAME="E3:30_4_1_2"/><b>then </b>
(  <a href="setwop_2.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> &amp;  <a href="setwop_2.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">A</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:30_4_1_2"/><b>then </b><i><font color="Green">E76</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font></span>)</span> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">A</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:30_4_1_2"/><b>then </b><i><font color="Green">E77</font></i>: 
(  <a href="matrix_1.html#K8">Line</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K9">Col</a> <font color="Maroon">B</font>,<font color="Maroon">i</font> &amp;  <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K8">Line</a> <font color="Maroon">A</font>,<font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="matrix_2.html#T16">MATRIX_2:16</a>, <a class="ref" href="matrix_2.html#T17">MATRIX_2:17</a></i>;<br/><a NAME="E6:30_4_1_2"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:30_4_1_2"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.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">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E8:30_4_1_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:30_4_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E10:30_4_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">j</font>,<font color="Maroon">i</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K3">dom</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="setwop_2.html#K2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><a NAME="E11:30_4_1_2"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">j</font>,<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"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrix_1.html#D5">MATRIX_1:def 5</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">B</font>,<font color="Maroon">i</font></span>)</span> <a href="fvsum_1.html#K13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <font color="Maroon">A</font>,<font color="Maroon">j</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <font color="Maroon">A</font>,<font color="Maroon">j</font></span>)</span> <a href="fvsum_1.html#K13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">B</font>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T115">FVSUM_1:115</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">j</font>,<font color="Maroon">i</font>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="matrix_1.html#D7">MATRIX_1:def 7</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E12:30"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</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">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_5"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_5_1"/>
(  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0 or  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_5_1_1"><b>suppose </b></a><a NAME="E1:30_5_1_1"/>
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_5_1_1"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</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">A</font>
 <b>by </b><i>, <a class="ref" href="matrix_1.html#D4">MATRIX_1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_5_1_2"><b>suppose </b></a><a NAME="E1:30_5_1_2"/>
 <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_5_1_2"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">A</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">A</font>
 <b>by </b><i><a class="ref" href="matrix_2.html#T12">MATRIX_2:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E13:30"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_3.html#K4" target="_self">*</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_1.html#K4">@</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="matrix_1.html#K4">@</a> </span>)</span> <a href="matrix_3.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrix_1.html#K4">@</a> </span>)</span>
 <b>by </b><i>, , , , , <a class="ref" href="matrix_1.html#T21">MATRIX_1:21</a></i>;<br/>


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