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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">M</font> being  <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Olive" title="b1">K</font><br/> for <font color="Olive" title="b3">nt</font>, <font color="Olive" title="b4">nt1</font>, <font color="Olive" title="b5">nt'</font>, <font color="Olive" title="b6">nt1'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b3">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b5">nt'</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b4">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b6">nt1'</font> &amp; not  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b3">nt</font>,<font color="Olive" title="b4">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b5">nt'</font>,<font color="Olive" title="b6">nt1'</font></span>)</span> holds <br/> <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b3">nt</font>,<font color="Olive" title="b4">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b5">nt'</font>,<font color="Olive" title="b6">nt1'</font></span>)</span></span>)</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">M</font> being  <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c2">K</font><br/> for <font color="Olive" title="b2">nt</font>, <font color="Olive" title="b3">nt1</font>, <font color="Olive" title="b4">nt'</font>, <font color="Olive" title="b5">nt1'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b4">nt'</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b3">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b5">nt1'</font> &amp; not  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b2">nt</font>,<font color="Olive" title="b3">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b4">nt'</font>,<font color="Olive" title="b5">nt1'</font></span>)</span> holds <br/> <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b2">nt</font>,<font color="Olive" title="b3">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b4">nt'</font>,<font color="Olive" title="b5">nt1'</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">M</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</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"> for <font color="Olive" title="b1">nt</font>, <font color="Olive" title="b2">nt1</font>, <font color="Olive" title="b3">nt'</font>, <font color="Olive" title="b4">nt1'</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b3">nt'</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b4">nt1'</font> &amp; not  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b3">nt'</font>,<font color="Olive" title="b4">nt1'</font></span>)</span> holds <br/> <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b2">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b3">nt'</font>,<font color="Olive" title="b4">nt1'</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">nt</font>, <font color="Maroon" title="c5">nt1</font>, <font color="Maroon" title="c6">nt'</font>, <font color="Maroon" title="c7">nt1'</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">nt'</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">nt1'</font> &amp; not  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> implies  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E36">A1</font></i>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">nt'</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">nt1'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c8">S</font> =  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font>;<br/>
<b>set </b><font color="Maroon" title="c9">S'</font> =  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font>;<br/>
<b>set </b><font color="Maroon" title="c10">S1'</font> =  <a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_1"/>
(  not <font color="Maroon" title="c4">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> or  not <font color="Maroon" title="c5">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> or ( <font color="Maroon" title="c4">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> &amp; <font color="Maroon" title="c5">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1"><b>suppose </b></a><a NAME="E1:38_1_1"/><i><font color="Green" title="E37">A2</font></i>: 
(  not <font color="Maroon" title="c4">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> or  not <font color="Maroon" title="c5">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:38_1_1"/><b>then </b>
(  not <font color="Maroon" title="c6">nt'</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> or  not <font color="Maroon" title="c7">nt1'</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="matrix13.html#E37"><i><font color="Green" title="E34">Lm1</font></i></a></i>;<br/><a NAME="E3:38_1_1"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font> &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font> )
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38_1_1"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="matrix13.html#T27" target="_self" title="MATRIX13:th.27">Th27</a>, <a class="ref" href="matrix13.html#T31" target="_self" title="MATRIX13:th.31">Th31</a></i>;<br/><b>hence </b><a NAME="E4:38_1_1"/>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )
 ; <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="38_1_2"><b>suppose </b></a><a NAME="E1:38_1_2"/><i><font color="Green" title="E37">A3</font></i>: 
( <font color="Maroon" title="c4">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> &amp; <font color="Maroon" title="c5">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:38_1_2"/><b>then </b>
<font color="Maroon" title="c6">nt'</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="matrix13.html#E37"><i><font color="Green" title="E34">Lm1</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c11">perm</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E4:38_1_2"/><i><font color="Green" title="E38">A4</font></i>: 
<font color="Maroon" title="c4">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">nt'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c11">perm</font>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="matrix13.html#E1:38_1_2"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="matrix13.html#T32" target="_self" title="MATRIX13:th.32">Th32</a></i>;<br/><a NAME="E5:38_1_2"/>
<font color="Maroon" title="c7">nt1'</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="matrix13.html#E1:38_1_2"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="matrix13.html#E37"><i><font color="Green" title="E34">Lm1</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">perm1</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E7:38_1_2"/><i><font color="Green" title="E39">A5</font></i>: 
<font color="Maroon" title="c5">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt1'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">perm1</font>
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="matrix13.html#E1:38_1_2"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="matrix13.html#T32" target="_self" title="MATRIX13:th.32">Th32</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">perm</font> = <font color="Maroon" title="c11">perm</font>, <font color="Maroon" title="c14">perm1</font> = <font color="Maroon" title="c12">perm1</font> as    <a href="matrix_2.html#M1" title="MATRIX_2:mode.1">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="matrix_2.html#D11" title="MATRIX_2:def.11">MATRIX_2:def 11</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_1_2_1"/>
( <font color="Maroon" title="c14">perm1</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> or  not <font color="Maroon" title="c14">perm1</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2_1_1"><b>suppose </b></a><a NAME="E1:38_1_2_1_1"/><i><font color="Green" title="E40">A6</font></i>: 
<font color="Maroon" title="c14">perm1</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:38_1_2_1_1"/>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span>,<font color="Maroon" title="c14">perm1</font> &amp; ( <font color="Maroon" title="c13">perm</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> or  not <font color="Maroon" title="c13">perm</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> ) &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span>,<font color="Maroon" title="c13">perm</font> )
 <b>by </b><i><a class="txt" href="matrix13.html#E4:38_1_2"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="matrix13.html#E7:38_1_2"><i><font color="Green" title="E39">A5</font></i></a>, <a class="ref" href="matrix13.html#T35" target="_self" title="MATRIX13:th.35">Th35</a></i>;<br/><a NAME="E3:38_1_2_1_1"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> &amp; (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38_1_2_1_1"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>;<br/><b>hence </b><a NAME="E4:38_1_2_1_1"/>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )
 ; <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="38_1_2_1_2"><b>suppose </b></a><a NAME="E1:38_1_2_1_2"/><i><font color="Green" title="E40">A7</font></i>: 
not <font color="Maroon" title="c14">perm1</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:38_1_2_1_2"/>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span>,<font color="Maroon" title="c14">perm1</font> &amp; ( <font color="Maroon" title="c13">perm</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> or  not <font color="Maroon" title="c13">perm</font> is <a href="matrix_2.html#V5" title="MATRIX_2:attr.5">even</a> ) &amp;  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_2.html#K14" title="MATRIX_2:func.14">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span>,<font color="Maroon" title="c13">perm</font> )
 <b>by </b><i><a class="txt" href="matrix13.html#E4:38_1_2"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="matrix13.html#E7:38_1_2"><i><font color="Green" title="E39">A5</font></i></a>, <a class="ref" href="matrix13.html#T35" target="_self" title="MATRIX13:th.35">Th35</a></i>;<br/><a NAME="E3:38_1_2_1_2"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> &amp; (  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="matrix13.html#E1:38_1_2_1_2"><i><font color="Green" title="E40">A7</font></i></a>, <a class="ref" href="matrix_2.html#D16" title="MATRIX_2:def.16">MATRIX_2:def 16</a></i>;<br/><a NAME="E4:38_1_2_1_2"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p4">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>;<br/><a NAME="E5:38_1_2_1_2"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p3">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span></span>)</span> )
 ;<br/><a NAME="E6:38_1_2_1_2"/><b>then </b>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> or <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p3">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font> )
 <b>by </b><i><a class="ref" href="vectsp_2.html#T22" title="VECTSP_2:th.22">VECTSP_2:22</a></i>;<br/><b>hence </b><a NAME="E7:38_1_2_1_2"/>
(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <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"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span> or  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">nt</font>,<font color="Maroon" title="c5">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c6">nt'</font>,<font color="Maroon" title="c7">nt1'</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="vectsp_1.html#T66" title="VECTSP_1:th.66">VECTSP_1:66</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></div><b>end;</b></div></div><b>end;</b></div>

</div>
