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<b>let </b><font color="Maroon">C1</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> , <font color="Maroon">C2</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:32_1_2"/><i><font color="Green">E31</font></i>: 
( ( for <font color="Olive">ea</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a>   st <font color="Olive">ea</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> holds <br/><font color="Maroon">C1</font> <a href="hidden.html#R1">=</a>  <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Olive">ea</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> ) &amp; ( for <font color="Olive">ea</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="vectsp_1.html#K3">F_Real</a>   st <font color="Olive">ea</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> holds <br/><font color="Maroon">C2</font> <a href="hidden.html#R1">=</a>  <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Olive">ea</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> ) )
 ;<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="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E3:32_1_2"/>
<font color="Maroon">C2</font> <a href="hidden.html#R1">=</a>  <a href="matrixr1.html#K2" target="_self">MXF2MXR</a> <span class="p1">(<span class="default"><font color="Maroon">aa</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/>
<b>hence </b><a NAME="E4:32_1_2"/>
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font>
 <b>by </b><i/>;<br/>


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