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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="firebrick">::  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">M1</font>, <font color="Olive" title="b3">M2</font>, <font color="Olive" title="b4">M3</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">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b3">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b4">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b4">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b4">M3</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">M3</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> <span class="p2">(<span class="default"><font color="Olive" title="b3">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span> )</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M1</font>, <font color="Olive" title="b2">M2</font>, <font color="Olive" title="b3">M3</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">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <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">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b1">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b2">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b2">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">M3</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">M3</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> <span class="p2">(<span class="default"><font color="Olive" title="b2">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span> )</span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c5">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  implies ( <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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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> ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c3">M1</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c4">M2</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<font color="Maroon" title="c5">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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> )</span><br/>

<a NAME="E4:67"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</a></span>;<br/>
<a NAME="E5:67"/><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<font color="Maroon" title="c4">M2</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="c4">M2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</a></span>;<br/>
<a NAME="E6:67"/><span class="lab"><font color="Green" title="E30">A6</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E7:67"/><span class="lab"><font color="Green" title="E31">A7</font></span>: 
<font color="Maroon" title="c5">M3</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="c5">M3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</a></span>;<br/>
<a NAME="E8:67"/><span class="lab"><font color="Green" title="E32">A8</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E9:67"/><span class="lab"><font color="Green" title="E33">A9</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E10:67"/><span class="lab"><font color="Green" title="E34">A10</font></span>: 
 <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#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E11:67"/><span class="lab"><font color="Green" title="E35">A11</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">M5</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">M4</font> = <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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font>;<br/>
<a NAME="E12:67"/><span class="lab"><font color="Green" title="E36">A12</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E13:67"/><span class="lab"><font color="Green" title="E37">A13</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E14:67"/><span class="lab"><font color="Green" title="E38">A14</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E15:67"/><span class="lab"><font color="Green" title="E39">A15</font></span>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</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> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E16:67"/><span class="lab"><font color="Green" title="E40">A16</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M3</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E17:67"/><span class="lab"><font color="Green" title="E41">A17</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E18:67"/><span class="lab"><font color="Green" title="E42">A18</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">M3</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E19:67"/><span class="lab"><font color="Green" title="E43">A19</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E20:67"/><span class="lab"><font color="Green" title="E44">A20</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E21:67"/><span class="lab"><font color="Green" title="E45">A21</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<a NAME="E22:67"/><span class="lab"><font color="Green" title="E46">A22</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E47">A23</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <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> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <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> <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="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E38">A14</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p4">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p3">(<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> <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="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E46">A22</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E37">A13</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<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="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M1</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E44">A20</font></span></a>, <a class="txt" href="#E19:67"><span class="lab"><font color="Green" title="E43">A19</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E35">A11</font></span></a>, <a class="txt" href="#E17:67"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<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></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T19" title="MATRIX_3:th.19">MATRIX_3:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E38">A14</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="txt" href="#E17:67"><span class="lab"><font color="Green" title="E41">A17</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</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="c4">M2</font></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E38">A14</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E42">A18</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<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></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">M3</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="c5">M3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T19" title="MATRIX_3:th.19">MATRIX_3:19</a></span>
<br/>.= 
 <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E31">A7</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</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> <span class="p3">(<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></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E42">A18</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E35">A11</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E42">A18</font></span></a>, <a class="txt" href="#E16:67"><span class="lab"><font color="Green" title="E40">A16</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E39">A15</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">M3</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E30">A6</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E34">A10</font></span></a>, <a class="txt" href="#E16:67"><span class="lab"><font color="Green" title="E40">A16</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<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></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</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> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E31">A7</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
<br/>.= 
<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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</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> <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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T19" title="MATRIX_3:th.19">MATRIX_3:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E34">A10</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E32">A8</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E35">A11</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<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="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></span>)</span></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E46">A22</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E36">A12</font></span></a>, <a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E38">A14</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E45">A21</font></span></a>, <a class="ref" href="matrix_3.html#T33" title="MATRIX_3:th.33">MATRIX_3:33</a></span>
<br/>.= 
<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"><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></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c3">M1</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#K5" title="MATRIX_6:func.5">~</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_3.html#T19" title="MATRIX_3:th.19">MATRIX_3:19</a></span>
<br/>.= 
 <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>
;<br/>
<a NAME="E25:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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> <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:67"><span class="lab"><font color="Green" title="E47">A23</font></span></a>, <a class="ref" href="matrix_6.html#D2" target="_self" title="MATRIX_6:def.2">Def2</a></span>;<br/>
<a NAME="E26:67"/><span class="kw">then </span>
<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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</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="ref" href="matrix_6.html#D3" target="_self" title="MATRIX_6:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:67"/>
( <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> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M3</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M3</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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a></span>)</span></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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:67"><span class="lab"><font color="Green" title="E48">A24</font></span></a>, <a class="ref" href="matrix_6.html#D4" target="_self" title="MATRIX_6:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
