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<b>let </b><font color="Maroon">A</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> , <font color="Maroon">B</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green">E31</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">B</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">B</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">B</font> )
 ;<br/>

 <a href="matrixr1.html#K8" target="_self">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">B</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K4" target="_self">-</a> <font color="Maroon">A</font></span>)</span>
<b>by </b><i>, <a class="ref" href="matrix_4.html#T2">MATRIX_4:2</a></i>
<br/>.= 
 <a href="matrixr1.html#K2" target="_self">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" target="_self">MXR2MXF</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2">-</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a>, </i>
<br/>.= 
 <a href="matrixr1.html#K2" target="_self">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" target="_self">MXR2MXF</a> <font color="Maroon">B</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="matrix_4.html#K1">-</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_4.html#D1">MATRIX_4:def 1</a></i>
<br/>.= 
<font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="matrix_4.html#T21">MATRIX_4:21</a>, </i>
;<br/>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="matrixr1.html#K8" target="_self">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font></span>)</span>
 ;<br/>


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