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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><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> ;<br/>



<b>assume </b><a NAME="E1:43"/><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> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<a NAME="E2:43"/><i><font color="Green">E54</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <a href="vectsp_1.html#K3">F_Real</a> ,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <a href="vectsp_1.html#K3">F_Real</a> ,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T24">MATRIX_1:24</a>, </i>;<br/>
<a NAME="E3:43"/><i><font color="Green">E55</font></i>: 
 <a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font> is   <a href="matrix_1.html#NM6">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">m</font>,<a href="vectsp_1.html#K3">F_Real</a> 
 
<b>by </b><i>, <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">D</font> =  <a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font> as   <a href="matrix_1.html#NM6">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">m</font>,<a href="vectsp_1.html#K3">F_Real</a>  <b>by </b><i>, <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/>
<span class="p1">(<span class="default"><a href="matrixr1.html#K8" target="_self">0_Rmatrix</a> <font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">A</font> = 
 <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K1">0.</a> <a href="vectsp_1.html#K3">F_Real</a> ,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a>, , </i>
<br/>.= 
<font color="Maroon">A</font>
<b>by </b><i><a class="ref" href="matrix_3.html#T6">MATRIX_3:6</a></i>
;<br/>
<b>hence </b><a NAME="E6:43"/>
( <font color="Maroon">A</font> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K8" target="_self">0_Rmatrix</a> <font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; <span class="p1">(<span class="default"><a href="matrixr1.html#K8" target="_self">0_Rmatrix</a> <font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="matrix_3.html#T6">MATRIX_3:6</a>, </i>;<br/>


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