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

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Olive" title="b2">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Olive" title="b2">a</font></span><br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Olive" title="b1">a</font></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>suppose </b></a><a NAME="E1:29_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:29_1_1"/><i><font color="Green" title="E16">A2</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>;<br/><a NAME="E3:29_1_1"/><b>then </b><i><font color="Green" title="E17">A3</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="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </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"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> &amp;  <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"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:29_1_1"><i><font color="Green" title="E15">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="E4:29_1_1"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">i</font>, <font color="Maroon" title="c5">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> )</span><br/>



<b>assume </b><a NAME="E1:29_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font></span><br/>

<a NAME="E2:29_1_1_1"/><b>then </b><i><font color="Green" title="E18">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</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"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_1.html#T27" title="MATRIX_1:th.27">MATRIX_1:27</a></i>;<br/>
<a NAME="E3:29_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">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="c1">n</font> &amp; <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E4:29_1_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E5:29_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">j</font>,<font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D7" title="MATRIX_1:def.7">MATRIX_1:def 7</a>, <a class="ref" href="matrix_2.html#T1" title="MATRIX_2:th.1">MATRIX_2:1</a></i>;<br/>
<b>hence </b><a NAME="E6:29_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c5">j</font>
 <b>by </b><i><a class="txt" href="#E2:29_1_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="matrix_2.html#T1" title="MATRIX_2:th.1">MATRIX_2:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:29_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="#E3:29_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="matrix_1.html#T21" title="MATRIX_1:th.21">MATRIX_1:21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2"><b>suppose </b></a><a NAME="E1:29_1_2"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span><br/><div class="add"><a NAME="E2:29_1_2"/><b>then </b>
(  <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"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:29_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font> <a href="matrix_2.html#K2" title="MATRIX_2:func.2">--&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="card_2.html#T83" title="CARD_2:th.83">CARD_2:83</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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