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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c4">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">mt</font>, <font color="Maroon" title="c6">mt1</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">m</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> ;<br/><b>let </b><font color="Maroon" title="c7">M</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c4">K</font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green" title="E29">A1</font></i>: 
( <font color="Maroon" title="c1">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="c2">m</font> &amp; <font color="Maroon" title="c3">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="c2">m</font> &amp; <font color="Maroon" title="c5">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">mt</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">j</font> )
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">j</font>
 ;<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="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font>;<br/>
<a NAME="E3:31"/>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<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="E4:31"/><b>then </b>
(  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span>,<font color="Maroon" title="c1">i</font> &amp;  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span>,<font color="Maroon" title="c3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span>,<font color="Maroon" title="c3">j</font> )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:31"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="matrix_2.html#T17" title="MATRIX_2:th.17">MATRIX_2:17</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
(  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span>,<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span>,<font color="Maroon" title="c3">j</font> &amp; ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">j</font> or <font color="Maroon" title="c3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> ) )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:31"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="matrix13.html#E2:31"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="matrix13.html#T29" target="_self" title="MATRIX13:th.29">Th29</a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/>
<b>hence </b> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">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="matrix13.html#K1" title="MATRIX13:func.1">Segm</a> <font color="Maroon" title="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix13.html#E1:31"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="matrix11.html#T50" title="MATRIX11:th.50">MATRIX11:50</a></i>
<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="c7">M</font>,<font color="Maroon" title="c6">mt1</font>,<font color="Maroon" title="c5">mt</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr2.html#T43" title="MATRIXR2:th.43">MATRIXR2:43</a></i>
;<br/><br/>


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