<?xml version="1.0"?>
<div class="add">

<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#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">K</font>  st <font color="Olive" title="b2">M</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> holds <br/>( <font color="Olive" title="b2">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M</font> )</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#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>  st <font color="Olive" title="b1">M</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> holds <br/>( <font color="Olive" title="b1">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M</font> )</span><br/><b>let </b><font color="Maroon" title="c3">M</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"> ( <font color="Maroon" title="c3">M</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> implies ( <font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> ) )</span><br/>





<b>assume </b><a NAME="E1:23"/>
<font color="Maroon" title="c3">M</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> )</span><br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c3">M</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">M</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</a></i>;<br/>
<a NAME="E3:23"/><b>then </b>
<font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D3" target="_self" title="MATRIX_6:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:23"/>
( <font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> )
 <b>by </b><i><a class="txt" href="matrix_6.html#E2:23"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</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>
