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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</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">M1</font>, <font color="Olive" title="b2">M2</font> being   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  st  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b1">M1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Olive" title="b2">M2</font> holds <br/><font color="Olive" title="b1">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c3">M1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c4">M2</font> implies <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
 <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c3">M1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c4">M2</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">Vn</font> = <font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Vm</font> = <font color="Maroon" title="c2">m</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">Bn</font> =  <a href="matrix13.html#K11" title="MATRIX13:func.11">MX2FinS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,<font color="Maroon" title="c1">n</font>)</span>)</span> as    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">n</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T45" title="MATRLIN2:th.45">MATRLIN2:45</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">Bm</font> =  <a href="matrix13.html#K11" title="MATRIX13:func.11">MX2FinS</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> (<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>,<font color="Maroon" title="c2">m</font>)</span>)</span> as    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">m</font> <a href="prvect_1.html#K7" title="PRVECT_1:func.7">-VectSp_over</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T45" title="MATRLIN2:th.45">MATRLIN2:45</a></span>;<br/>
<a NAME="E4:50"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">Bn</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="matrtop1.html#T19" target="_self" title="MATRTOP1:th.19">Th19</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">A1</font> = <font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c10">B1</font> = <font color="Maroon" title="c4">M2</font> as   <a href="matrix_1.html#NM6" title="MATRIX_1:NM.6">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">Bn</font>, <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">Bm</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T19" target="_self" title="MATRTOP1:th.19">Th19</a></span>;<br/>
<span class="lab"><font color="Green" title="E28">A2</font></span>:  <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c9">A1</font>,<font color="Maroon" title="c7">Bn</font>,<font color="Maroon" title="c8">Bm</font>) = 
 <a href="matrtop1.html#K3" title="MATRTOP1:func.3">Mx2Tran</a> <font color="Maroon" title="c3">M1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrtop1.html#T20" target="_self" title="MATRTOP1:th.20">Th20</a></span>
<br/>.= 
 <a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c10">B1</font>,<font color="Maroon" title="c7">Bn</font>,<font color="Maroon" title="c8">Bm</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="matrtop1.html#T20" target="_self" title="MATRTOP1:th.20">Th20</a></span>
;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">M1</font> = 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> (<span class="p1">(<span class="default"><a href="matrlin2.html#K4" title="MATRLIN2:func.4">Mx2Tran</a> (<font color="Maroon" title="c9">A1</font>,<font color="Maroon" title="c7">Bn</font>,<font color="Maroon" title="c8">Bm</font>)</span>)</span>,<font color="Maroon" title="c7">Bn</font>,<font color="Maroon" title="c8">Bm</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T36" title="MATRLIN2:th.36">MATRLIN2:36</a></span>
<br/>.= 
<font color="Maroon" title="c4">M2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="matrlin2.html#T36" title="MATRLIN2:th.36">MATRLIN2:36</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/>


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