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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <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>   st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">A</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="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> holds <br/><span class="p1">(<span class="default"><a href="matrixr1.html#K4" title="MATRIXR1:func.4">-</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span><br/><b>let </b><font color="Maroon" title="c3">A</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">A</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="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> implies <span class="p1">(<span class="default"><a href="matrixr1.html#K4" title="MATRIXR1:func.4">-</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> )</span><br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E29">A1</font></i>: 
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">A</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="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrixr1.html#K4" title="MATRIXR1:func.4">-</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font></span><br/>

<a NAME="E2:33"/><i><font color="Green" title="E30">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> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font></span>)</span></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="c3">A</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/>
<a NAME="E3:33"/>
 <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> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font></span>)</span></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="c3">A</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/>
<b>hence </b><span class="p1">(<span class="default"><a href="matrixr1.html#K4" title="MATRIXR1:func.4">-</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="matrixr1.html#K3" title="MATRIXR1:func.3">+</a> <font color="Maroon" title="c3">A</font> = 
 <a href="matrixr1.html#K2" title="MATRIXR1:func.2">MXF2MXR</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font></span>)</span> <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> <span class="p3">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:33"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="matrix_3.html#T4" title="MATRIX_3:th.4">MATRIX_3:4</a></i>
<br/>.= 
 <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>
<b>by </b><i><a class="txt" href="#E1:33"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="matrix_4.html#T2" title="MATRIX_4:th.2">MATRIX_4:2</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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