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

<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c3">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c4">k</font>, <font color="Maroon" title="c5">l</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c6">M</font>, <font color="Maroon" title="c7">M1</font>, <font color="Maroon" title="c8">M2</font> be   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c3">K</font>;<br/><b>let </b><font color="Maroon" title="c9">pK</font>, <font color="Maroon" title="c10">qK</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">K</font>;<br/><b>let </b><font color="Maroon" title="c11">i</font>, <font color="Maroon" title="c12">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>























<b>assume </b><a NAME="E1:1"/><i><font color="Green" title="E2">A1</font></i>: 
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c12">j</font> <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> <font color="Maroon" title="c6">M</font></span>)</span> &amp; <font color="Maroon" title="c9">pK</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c10">qK</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">k</font> &amp; <font color="Maroon" title="c7">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c9">pK</font> &amp; <font color="Maroon" title="c8">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> <font color="Maroon" title="c7">M1</font>,<font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c10">qK</font> )
 ;<br/>

<b>thus </b><a NAME="E2:1"/>
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> implies <font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c12">j</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_1"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font>
 ;<br/>

<a NAME="E2:1_1"/><i><font color="Green" title="E4">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">pK</font> <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="c6">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">qK</font> <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="c6">M</font> )
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>;<br/>
<a NAME="E3:1_1"/><b>then </b><i><font color="Green" title="E5">A4</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c6">M</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<a NAME="E4:1_1"/><b>then </b><i><font color="Green" title="E6">A4a</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c8">M2</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E2:1_1"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E3:1_1"><i><font color="Green" title="E5">A4</font></i></a>, <a class="txt" href="matrix12.html#E4:1_1"><i><font color="Green" title="E6">A4a</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c10">qK</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="matrix12.html#E2:1_1"><i><font color="Green" title="E4">A3</font></i></a>, <a class="txt" href="matrix12.html#E3:1_1"><i><font color="Green" title="E5">A4</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>
<br/>.= 
<font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:1"/>
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font> implies <font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c12">j</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_2"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font>
 ;<br/>

<a NAME="E2:1_2"/><i><font color="Green" title="E4">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">pK</font> <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="c6">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">qK</font> <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="c6">M</font> )
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>;<br/>
<a NAME="E3:1_2"/><b>then </b><i><font color="Green" title="E5">A4</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c6">M</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<a NAME="E4:1_2"/><b>then </b><i><font color="Green" title="E6">A4a</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c8">M2</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E2:1_2"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<a NAME="E5:1_2"/><i><font color="Green" title="E7">A5</font></i>: 
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font> implies  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M1</font>,<font color="Maroon" title="c11">i</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_2_1"/><i><font color="Green" title="E8">A5aa</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:1_2_1_1"/>
( <font color="Maroon" title="c5">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">k</font> or <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_2_1_1_1"><b>suppose </b></a><a NAME="E1:1_2_1_1_1"/>
<font color="Maroon" title="c5">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">k</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_2_1_1_1"/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M1</font>,<font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_2_1"><i><font color="Green" title="E8">A5aa</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_2_1_1_2"><b>suppose </b></a><a NAME="E1:1_2_1_1_2"/>
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font>
 ;<br/><div class="add"><a NAME="E2:1_2_1_1_2"/><b>then </b>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">pK</font>
 <b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="matrix12.html#E2:1_2"><i><font color="Green" title="E4">A3</font></i></a>, <a class="txt" href="matrix12.html#E3:1_2"><i><font color="Green" title="E5">A4</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>;<br/><b>hence </b><a NAME="E3:1_2_1_1_2"/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M1</font>,<font color="Maroon" title="c11">i</font>
 <b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="matrix12.html#E2:1_2"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>thus </b><font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E3:1_2"><i><font color="Green" title="E5">A4</font></i></a>, <a class="txt" href="matrix12.html#E4:1_2"><i><font color="Green" title="E6">A4a</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c9">pK</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E5:1_2"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="matrix12.html#E2:1_2"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>
<br/>.= 
<font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">l</font>,<font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:1"/>
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">k</font> implies <font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_3"/><i><font color="Green" title="E3">A2</font></i>: 
( <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">l</font> &amp; <font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">k</font> )
 ;<br/>

<a NAME="E2:1_3"/><i><font color="Green" title="E4">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">pK</font> <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="c6">M</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">qK</font> <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="c6">M</font> )
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>;<br/>
<a NAME="E3:1_3"/><b>then </b><i><font color="Green" title="E5">A4</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c6">M</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<a NAME="E4:1_3"/><b>then </b><i><font color="Green" title="E6">A4a</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c7">M1</font> <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="c8">M2</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E2:1_3"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="matrix11.html#D3" title="MATRIX11:def.3">MATRIX11:def 3</a></i>;<br/>
<a NAME="E5:1_3"/><i><font color="Green" title="E7">A6</font></i>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c7">M1</font>,<font color="Maroon" title="c11">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c11">i</font>
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_3"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c8">M2</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c8">M2</font>,<font color="Maroon" title="c11">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E3:1_3"><i><font color="Green" title="E5">A4</font></i></a>, <a class="txt" href="matrix12.html#E4:1_3"><i><font color="Green" title="E6">A4a</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c6">M</font>,<font color="Maroon" title="c11">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="matrix12.html#E1:1_3"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="matrix11.html#T28" title="MATRIX11:th.28">MATRIX11:28</a>, <a class="txt" href="matrix12.html#E5:1_3"><i><font color="Green" title="E7">A6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">M</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c11">i</font>,<font color="Maroon" title="c12">j</font>
<b>by </b><i><a class="txt" href="matrix12.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
;<br/>


</div><b>end;</b></div>


</div>
