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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">M1</font>, <font color="Maroon" title="c3">M2</font>, <font color="Maroon" title="c4">M3</font> be   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font>;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E18">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">M3</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M2</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">M3</font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b><i><font color="Green" title="E19">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2" title="MATRIX_3:func.2">-</a> <font color="Maroon" title="c4">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">M1</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2" title="MATRIX_3:func.2">-</a> <font color="Maroon" title="c4">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c2">M1</font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D2" title="MATRIX_3:def.2">MATRIX_3:def 2</a></i>;<br/>
<font color="Maroon" title="c2">M1</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M2</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <font color="Maroon" title="c4">M3</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">M1</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <font color="Maroon" title="c3">M2</font></span>)</span> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2" title="MATRIX_3:func.2">-</a> <font color="Maroon" title="c4">M3</font></span>)</span>
<b>by </b><i><a class="txt" href="matrix_4.html#E1:31"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="matrix_4.html#E2:31"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="matrix_4.html#T31" target="_self" title="MATRIX_4:th.31">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">M1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K2" title="MATRIX_3:func.2">-</a> <font color="Maroon" title="c3">M2</font></span>)</span></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c4">M3</font>
<b>by </b><i><a class="ref" href="matrix_4.html#T1" target="_self" title="MATRIX_4:th.1">Th1</a></i>
;<br/>
<b>hence </b><a NAME="E4:31"/>
<font color="Maroon" title="c2">M1</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M2</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <font color="Maroon" title="c4">M3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">M1</font> <a href="matrix_4.html#K1" title="MATRIX_4:func.1">-</a> <font color="Maroon" title="c3">M2</font></span>)</span> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Maroon" title="c4">M3</font>
 ;<br/>


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