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<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">M</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>reconsider </b><font color="Maroon" title="c3">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>  ;<br/>
<b>let </b><font color="Maroon" title="c4">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E2:64"/><i><font color="Green" title="E27">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font> &amp; <font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M</font> )
 ;<br/>

 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</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">M</font></span>)</span>,<font color="Maroon" title="c4">i</font> = 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">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">M</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c4">i</font>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</a></i>
<br/>.= 
<font color="Maroon" title="c3">ea</font> <a href="fvsum_1.html#K10" title="FVSUM_1:func.10">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c2">M</font></span>)</span>,<font color="Maroon" title="c4">i</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#T19" target="_self" title="MATRIXR1:th.19">Th19</a>, <a class="txt" href="matrixr1.html#E2:64"><i><font color="Green" title="E27">A1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E4:64"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</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">M</font></span>)</span>,<font color="Maroon" title="c4">i</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">a</font> <a href="rvsum_1.html#K11" title="RVSUM_1:func.11">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrixr1.html#T17" target="_self" title="MATRIXR1:th.17">Th17</a></i>;<br/>


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