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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> ;<br/>

<b>reconsider </b><font color="Maroon">e3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a>  ;<br/>
<a NAME="E2:40"/><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> <span class="p1">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span> )
 
;<br/>
<i><font color="Green">E54</font></i>: <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> = 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K2">.</a> 1,1
<b>by </b><i><a class="ref" href="vectsp_1.html#T20">VECTSP_1:20</a></i>
<br/>.= 
1 <a href="binop_2.html#K23">+</a> 1
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">rr</font> = 1 <a href="binop_2.html#K23">+</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  ;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> = 
<a href="binop_2.html#K33">addreal</a>  <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K23">+</a> 1</span>)</span>,1
<b>by </b><i>, <a class="ref" href="vectsp_1.html#T20">VECTSP_1:20</a></i>
<br/>.= 
<font color="Maroon">rr</font> <a href="binop_2.html#K9">+</a> 1
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>
<br/>.= 
3

;<br/>
<b>then </b>3 <a href="matrixr1.html#K7" 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">e3</font> <a href="matrix_3.html#K6">*</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/>
<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="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span></span>)</span> <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></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T13">MATRIX_5:13</a></i>
<br/>.= 
 <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> <font color="Maroon">A</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span></span>)</span> <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></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10">MATRIX_5:10</a></i>
<br/>.= 
 <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> <font color="Maroon">A</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="matrix_3.html#K6">*</a> <span class="p4">(<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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="matrix_3.html#K6">*</a> <span class="p4">(<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>
<b>by </b><i><a class="ref" href="matrix_5.html#T13">MATRIX_5:13</a></i>
<br/>.= 
 <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> <font color="Maroon">A</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="vectsp_1.html#K3">F_Real</a> </span>)</span> <a href="matrix_3.html#K6">*</a> <span class="p4">(<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>
<b>by </b><i><a class="ref" href="matrix_5.html#T10">MATRIX_5:10</a></i>
<br/>.= 
 <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> <font color="Maroon">A</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">A</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></span>)</span>
<b>by </b><i><a class="ref" href="matrix_5.html#T10">MATRIX_5:10</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">A</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="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_3.html#T5">MATRIX_3:5</a>, </i>
;<br/>
<b>hence </b><a NAME="E7:40"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">A</font></span>)</span> <a href="matrixr1.html#K3" target="_self">+</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 3 <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">A</font>
 ;<br/>


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