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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</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> , <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="E1:50"/><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 )
 ;<br/>

<b>reconsider </b><font color="Maroon">ea</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<i><font color="Green">E54</font></i>: <font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <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#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</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"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T36">MATRIX_5:36</a>, </i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">A</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">B</font></span>)</span> = 
 <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p4">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</a> <span class="p5">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</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="matrixr1.html#K1" target="_self">MXR2MXF</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p4">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</a> <span class="p5">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</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"><font color="Maroon">ea</font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">B</font></span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E5:50"/>
<font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <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="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">A</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">B</font></span>)</span>
 <b>by </b><i/>;<br/>


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