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<b>let </b><font color="Maroon" title="c1">l</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">k</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>assume </b><a NAME="E1:37"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c1">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:37"/><i><font color="Green" title="E27">A2</font></i>: 
<span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#T10" title="MATRIX_6:th.10">MATRIX_6:10</a></i>;<br/>
<a NAME="E3:37"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</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="E4:37"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></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="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:37"/><i><font color="Green" title="E29">A4</font></i>: 
(  <a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font> )
 
<b>by </b><i><a class="txt" href="matrix12.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="matrix12.html#T12" target="_self" title="MATRIX12:th.12">Th12</a></i>;<br/>
 <a href="matrix12.html#NK10" title="MATRIX12:NK.10">ICol</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font> = 
<span class="p1">(<span class="default"><a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> 
<b>by </b><i><a class="txt" href="matrix12.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="matrix12.html#E2:37"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="matrix12.html#E4:37"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="matrix12.html#T15" target="_self" title="MATRIX12:th.15">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> 
<b>by </b><i><a class="txt" href="matrix12.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="matrix12.html#E5:37"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="matrix_6.html#T13" title="MATRIX_6:th.13">MATRIX_6:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix12.html#NK4" title="MATRIX12:NK.4">ILine</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> 
<b>by </b><i><a class="ref" href="matrix_6.html#T10" title="MATRIX_6:th.10">MATRIX_6:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix12.html#NK10" title="MATRIX12:NK.10">ICol</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> 
<b>by </b><i><a class="txt" href="matrix12.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="matrix12.html#E4:37"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="matrix12.html#T15" target="_self" title="MATRIX12:th.15">Th15</a></i>
;<br/>
<b>hence </b><a NAME="E7:37"/>
<span class="p1">(<span class="default"><a href="matrix12.html#NK10" title="MATRIX12:NK.10">ICol</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font></span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix12.html#NK10" title="MATRIX12:NK.10">ICol</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c1">l</font>,<font color="Maroon" title="c3">k</font>
 ;<br/>


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