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<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">N</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">K</font> holds   <a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b2">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b2">N</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></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">N</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font> holds   <a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Olive" title="b1">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Olive" title="b1">N</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c3">N</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<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">  <a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c3">N</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span><br/>





<b>set </b><font color="Maroon" title="c4">F</font> = <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span>;<br/>
<a NAME="E1:81"/><i><font color="Green" title="E54">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E2:81"/><i><font color="Green" title="E55">A2</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></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="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a>, <a class="ref" href="finseq_2.html#T144" title="FINSEQ_2:th.144">FINSEQ_2:144</a></i>;<br/>
<a NAME="E3:81"/>
( <span class="p1">(<span class="default"><a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><span class="p2"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> 1</span>)</span> &amp; <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">n</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="c3">N</font> )
 
<b>by </b><i><a class="txt" href="#E1:81"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="#E2:81"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="matrixj1.html#D7" target="_self" title="MATRIXJ1:def.7">Def7</a>, <a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a>, <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="E4:81"/>
 <a href="matrixj1.html#K22" title="MATRIXJ1:func.22">Det</a> <span class="p1"><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">&lt;*</a><span class="default"><font color="Maroon" title="c3">N</font></span><a href="matrixj1.html#K16" title="MATRIXJ1:func.16">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c3">N</font></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E1:81"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="#E2:81"><i><font color="Green" title="E55">A2</font></i></a>, <a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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