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

<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">c</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c4">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c5">AD</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c6">pD</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c7">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>













<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K2" title="SETWOP_2: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="c5">AD</font></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c7">i</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">R</font> =  <a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font>;<br/>
<b>set </b><font color="Maroon" title="c10">CR</font> =  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font>;<br/>
<b>set </b><font color="Maroon" title="c11">CA</font> =  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font>;<br/>
<b>thus </b><a NAME="E3:20"/>
( <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</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="c5">AD</font> implies  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pD</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</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="c5">AD</font> )
 ;<br/>

<a NAME="E2:20_1"/><i><font color="Green" title="E20">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</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="c6">pD</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</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="c5">AD</font> )
 
<b>by </b><i><a class="txt" href="laplace.html#E1:20_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="laplace.html#D2" target="_self" title="LAPLACE:def.2">DEF1</a></i>;<br/>
<a NAME="E3:20_1"/><b>then </b><i><font color="Green" title="E21">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</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="c6">pD</font>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">J</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:20_1_1"/><i><font color="Green" title="E22">A5</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">J</font> &amp; <font color="Maroon" title="c12">J</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font> )
 ;<br/><a NAME="E2:20_1_1"/>
<font color="Maroon" title="c12">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K2" title="SETWOP_2:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font></span>)</span>
 <b>by </b><i><a class="txt" href="laplace.html#E1:20_1_1"><i><font color="Green" title="E22">A5</font></i></a></i>;<br/><a NAME="E3:20_1_1"/><b>then </b>
( <font color="Maroon" title="c12">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> &amp; <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K2" title="SETWOP_2: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"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="laplace.html#E1:20"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="laplace.html#E2:20_1"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:20_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c12">J</font>,<font color="Maroon" title="c3">c</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">J</font>,<font color="Maroon" title="c3">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">AD</font> )
 <b>by </b><i><a class="txt" href="laplace.html#E1:20_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a>, <a class="ref" href="matrix_1.html#T27" title="MATRIX_1:th.27">MATRIX_1:27</a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pD</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="laplace.html#E1:20_1"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="laplace.html#D2" target="_self" title="LAPLACE:def.2">DEF1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">pD</font>
 <b>by </b><i><a class="txt" href="laplace.html#E3:20_1"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>


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

<b>assume </b><a NAME="E4:20"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">c</font>
 ;<br/>

<a NAME="E5:20"/><i><font color="Green" title="E20">A3</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</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="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">AD</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">AD</font> <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="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:20_2"/><i><font color="Green" title="E21">A4</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font></span>)</span> )
 ;<br/><a NAME="E2:20_2"/>
<font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setwop_2.html#K2" title="SETWOP_2:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">AD</font></span>)</span>
 <b>by </b><i><a class="txt" href="laplace.html#E5:20"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="laplace.html#E1:20_2"><i><font color="Green" title="E21">A4</font></i></a></i>;<br/><a NAME="E3:20_2"/><b>then </b>
( <font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <font color="Maroon" title="c5">AD</font> &amp; <font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finsop_1.html#K5" title="FINSOP_1:func.5">dom</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> )
 <b>by </b><i><a class="txt" href="laplace.html#E5:20"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:20_2"/><b>then </b><i><font color="Green" title="E22">A5</font></i>: 
( <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">AD</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c7">i</font> &amp; <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c7">i</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">j</font>,<font color="Maroon" title="c7">i</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">AD</font> )
 <b>by </b><i><a class="txt" href="laplace.html#E1:20"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_2_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</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="c5">AD</font> or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">AD</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1_1"><b>suppose </b></a><a NAME="E1:20_2_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</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="c5">AD</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_2_1_1"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">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="laplace.html#E4:20"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="laplace.html#E4:20_2"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="laplace.html#D2" target="_self" title="LAPLACE:def.2">DEF1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_2_1_2"><b>suppose </b></a><a NAME="E1:20_2_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">pD</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">AD</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_2_1_2"/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">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="ref" href="laplace.html#D2" target="_self" title="LAPLACE:def.2">DEF1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:20"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="laplace.html#NK4" title="LAPLACE:NK.4">RCol</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">pD</font></span>)</span>,<font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">AD</font>,<font color="Maroon" title="c7">i</font>
 <b>by </b><i><a class="txt" href="laplace.html#E5:20"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>


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