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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">M2</font>, <font color="Olive" title="b3">M1</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">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b3">M1</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Olive" title="b2">M2</font> holds <br/><font color="Olive" title="b3">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> </span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">M2</font>, <font color="Olive" title="b2">M1</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">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b2">M1</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Olive" title="b1">M2</font> holds <br/><font color="Olive" title="b2">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">M2</font>, <font color="Maroon" title="c4">M1</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c4">M1</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Maroon" title="c3">M2</font> implies <font color="Maroon" title="c4">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:45"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c3">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">and </span><br/><a NAME="E2:45"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c4">M1</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Maroon" title="c3">M2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">M4</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><span class="kw"> such that </span><br/><a NAME="E4:45"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
<font color="Maroon" title="c5">M4</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">and </span><br/><a NAME="E5:45"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c4">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:45"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="matrix_8.html#D5" target="_self" title="MATRIX_8:def.5">Def5</a></span>;<br/>
<a NAME="E6:45"/>
<font color="Maroon" title="c5">M4</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="matrix_6.html#T16" title="MATRIX_6:th.16">MATRIX_6:16</a></span>;<br/>
<a NAME="E7:45"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="matrix_6.html#T37" title="MATRIX_6:th.37">MATRIX_6:37</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:45"/>
<font color="Maroon" title="c4">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:45"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E5:45"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="matrix_6.html#T37" title="MATRIX_6:th.37">MATRIX_6:37</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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