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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</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>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>  ;<br/>
<b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E2:66"/><i><font color="Green">E31</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> )
 ;<br/>

 <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">M</font></span>)</span>,<font color="Maroon">i</font> = 
 <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K2" target="_self">MXF2MXR</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">M</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">i</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">ea</font> <a href="fvsum_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" target="_self">MXR2MXF</a> <font color="Maroon">M</font></span>)</span>,<font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E4:66"/>
 <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrixr1.html#K7" target="_self">*</a> <font color="Maroon">M</font></span>)</span>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rvsum_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">M</font>,<font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/>


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