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

<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V1</font> being  <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">b19</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font> holds <br/> (  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span>,<font color="Olive" title="b3">b19</font>,<font color="Olive" title="b2">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b1</font>, <font color="Olive" title="b2">b19</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font> holds <br/> (  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Olive" title="b2">b19</font>,<font color="Olive" title="b1">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">b19</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">A</font> =  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font>;<br/>
<a NAME="E1:36"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
 
;<br/>
<span class="lab"><font color="Green" title="E21">A2</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font> = 
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b19</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">A9</font> =  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> as   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E4:36"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
(  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> &amp; <font color="Maroon" title="c6">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="matrlin2.html#D2" target="_self" title="MATRLIN2:def.2">Def2</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_2"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1"><span class="kw">suppose </span></a><a NAME="E1:36_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )</span><br/><div class="add"><a NAME="E2:36_2_1"/><span class="kw">then </span>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> &amp; <font color="Maroon" title="c6">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixr2.html#T41" title="MATRIXR2:th.41">MATRIXR2:41</a>, <a class="ref" href="matrix_1.html#T36" title="MATRIX_1:th.36">MATRIX_1:36</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_2_1"/>
(  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="laplace.html#T34" title="LAPLACE:th.34">LAPLACE:34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_2"><span class="kw">suppose </span></a><a NAME="E1:36_2_2"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )</span><br/><div class="add"><a NAME="E2:36_2_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>;<br/><a NAME="E3:36_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A5</font></span>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>;<br/><a NAME="E4:36_2_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>;<br/><a NAME="E5:36_2_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</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="c4">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" target="_self" title="MATRLIN2:th.21">Th21</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A6</font></span>: <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">A9</font> = 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c3">b1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E1:36_2_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="matrlin.html#T46" title="MATRLIN:th.46">MATRLIN:46</a></span>
<br/>.= 
 <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c1">K</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_2_2"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="matrlin2.html#T28" target="_self" title="MATRLIN2:th.28">Th28</a></span>
;<br/><a NAME="E7:36_2_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_2_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="nat_1.html#T19" title="NAT_1:th.19">NAT_1:19</a></span>;<br/><span class="kw">then </span> <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> = 
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">A9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_2_2"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="matrix_7.html#T16" title="MATRIX_7:th.16">MATRIX_7:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c6">A9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_2_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="matrix11.html#T62" title="MATRIX11:th.62">MATRIX11:62</a></span>
;<br/><a NAME="E9:36_2_2"/><span class="kw">then </span>
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T44" title="VECTSP_1:th.44">VECTSP_1:44</a></span>;<br/><a NAME="E10:36_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A7</font></span>: 
 <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="laplace.html#T34" title="LAPLACE:th.34">LAPLACE:34</a></span>;<br/><a NAME="E11:36_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</a>  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#D4" title="MATRIX_6:def.4">MATRIX_6:def 4</a></span>;<br/><a NAME="E12:36_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c1">K</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">b1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E13:36_2_2"/>
(  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp;  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c4">b19</font>,<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">b19</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_2_2"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E10:36_2_2"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="matrix_8.html#T19" title="MATRIX_8:th.19">MATRIX_8:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
