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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</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="E1:42"/><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="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Maroon" title="c1">A</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c2">B</font> )
 ;<br/>

<b>then </b> <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K4" title="MATRIXR1:func.4">-</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_4.html#T2" title="MATRIX_4:th.2">MATRIX_4:2</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2" title="MATRIX_3:func.2">-</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></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#E1:42"><i><font color="Green" title="E15">A1</font></i></a></i>
<br/>.= 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_4.html#D1" title="MATRIX_4:def.1">MATRIX_4:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c2">B</font>
<b>by </b><i><a class="ref" href="matrix_4.html#T21" title="MATRIX_4:th.21">MATRIX_4:21</a>, <a class="txt" href="matrixr1.html#E1:42"><i><font color="Green" title="E15">A1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E3:42"/>
<font color="Maroon" title="c2">B</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span>
 ;<br/>


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