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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">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="E1:48"/><i><font color="Green" title="E16">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">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="c3">B</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">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="c3">B</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">A</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">ea</font> = <font color="Maroon" title="c1">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<i><font color="Green" title="E17">A2</font></i>: <font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">B</font></span>)</span> = 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</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"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrixr1.html#E1:48"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="matrix_5.html#T36" title="MATRIX_5:th.36">MATRIX_5:36</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c3">B</font></span>)</span> = 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p5">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</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"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">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="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p5">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</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"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">ea</font> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E5:48"/>
<font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c3">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrixr1.html#E3:48"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>


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