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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:20"/><i><font color="Green">E42</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7">*</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7">*</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <font color="Maroon">M</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">aa</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="vectsp_1.html#D15">VECTSP_1:def 15</a></i>;<br/>
<i><font color="Green">E43</font></i>:  <a href="matrixr1.html#K1">MXR2MXF</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7">*</a> <font color="Maroon">M</font></span>)</span> = 
 <a href="matrixr1.html#K1">MXR2MXF</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K2">MXF2MXR</a> <span class="p2">(<span class="default"><font color="Maroon">aa</font> <a href="matrix_3.html#K6">*</a> <span class="p3">(<span class="default"><a href="matrixr1.html#K1">MXR2MXF</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7">MATRIXR1:def 7</a></i>
<br/>.= 
<font color="Maroon">aa</font> <a href="matrix_3.html#K6">*</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K1">MXR2MXF</a> <font color="Maroon">M</font></span>)</span>

;<br/>
<a NAME="E4:20"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7">*</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">aa</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1">MXR2MXF</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrix_3.html#D5">MATRIX_3:def 5</a>, , , <a class="ref" href="vectsp_1.html#D15">VECTSP_1:def 15</a></i>;<br/>
<b>hence </b><a NAME="E5:20"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7">*</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp_1.html#D15">VECTSP_1:def 15</a>, <a class="ref" href="binop_2.html#D11">BINOP_2:def 11</a></i>;<br/>


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