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<b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E15">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">A</font> <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> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> &amp; <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:43"/><i><font color="Green" title="E16">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">F_Real</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</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"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">F_Real</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a>, <a class="txt" href="matrixr1.html#E1:43"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<a NAME="E3:43"/><i><font color="Green" title="E17">A3</font></i>: 
 <a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font> is   <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#K3" title="VECTSP_1:func.3">F_Real</a> 
 
<b>by </b><i><a class="txt" href="matrixr1.html#E1:43"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="matrix_1.html#T20" title="MATRIX_1:th.20">MATRIX_1:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">D</font> =  <a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font> as   <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#K3" title="VECTSP_1:func.3">F_Real</a>  <b>by </b><i><a class="txt" href="matrixr1.html#E1:43"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="matrix_1.html#T20" title="MATRIX_1:th.20">MATRIX_1:20</a></i>;<br/>
<span class="p1">(<span class="default"><a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">A</font> = 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">F_Real</a> ,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T4" title="MATRIX_3:th.4">MATRIX_3:4</a>, <a class="txt" href="matrixr1.html#E1:43"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="matrixr1.html#E2:43"><i><font color="Green" title="E16">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font>
<b>by </b><i><a class="ref" href="matrix_3.html#T6" title="MATRIX_3:th.6">MATRIX_3:6</a></i>
;<br/>
<b>hence </b><a NAME="E6:43"/>
( <font color="Maroon" title="c3">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> )
 <b>by </b><i><a class="ref" href="matrix_3.html#T6" title="MATRIX_3:th.6">MATRIX_3:6</a>, <a class="txt" href="matrixr1.html#E3:43"><i><font color="Green" title="E17">A3</font></i></a></i>;<br/>


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