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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>;<br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font>, <font color="Maroon" title="c5">M3</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>;<br/>









<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c3">M1</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M1</font> )
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c3">M1</font> <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> <font color="Maroon" title="c3">M1</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D4" title="MATRIX_6:def.4">MATRIX_6:def 4</a></i>;<br/>
<a NAME="E3:22"/><i><font color="Green" title="E10">A3</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">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="E4:22"/><i><font color="Green" title="E11">A4</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">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="E5:22"/><i><font color="Green" title="E12">A5</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">M3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">M3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">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="E6:22"/><i><font color="Green" title="E13">A6</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">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/>
<font color="Maroon" title="c4">M2</font> = 
<font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T21" title="MATRIX_3:th.21">MATRIX_3:21</a></i>
<br/>.= 
<font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E2:22"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E1:22"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="matrix_8.html#E4:22"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="matrix_8.html#E3:22"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="matrix_8.html#E6:22"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="matrix_3.html#T35" title="MATRIX_3:th.35">MATRIX_3:35</a></i>
<br/>.= 
<font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E3:22"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="matrix_8.html#E5:22"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="matrix_8.html#E6:22"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="matrix_3.html#T35" title="MATRIX_3:th.35">MATRIX_3:35</a></i>
<br/>.= 
<font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_8.html#E2:22"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c5">M3</font>
<b>by </b><i><a class="ref" href="matrix_3.html#T21" title="MATRIX_3:th.21">MATRIX_3:21</a></i>
;<br/>
<b>hence </b><a NAME="E8:22"/>
<font color="Maroon" title="c4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M3</font>
 ;<br/>


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