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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#R1" title="MATRIX_6:pred.1">commutes_with</a> <font color="Maroon" title="c4">M2</font> )
 ;<br/>

<a NAME="E2:60"/><i><font color="Green" title="E25">A2</font></i>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E1:60"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="matrix_4.html#T63" title="MATRIX_4:th.63">MATRIX_4:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M1</font></span>)</span> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E1:60"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="matrix_6.html#D1" target="_self" title="MATRIX_6:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_6.html#E1:60"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="matrix_6.html#E2:60"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="matrix_4.html#T62" title="MATRIX_4:th.62">MATRIX_4:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:60"/>
<font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K2" title="MATRIX_6:func.2">+</a> <font color="Maroon" title="c4">M2</font> <a href="matrix_6.html#R1" title="MATRIX_6:pred.1">commutes_with</a> <font color="Maroon" title="c4">M2</font>
 <b>by </b><i><a class="ref" href="matrix_6.html#D1" target="_self" title="MATRIX_6:def.1">Def1</a></i>;<br/>


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