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<b>let </b><font color="Maroon" title="c1">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"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</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>  implies <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E16">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span></span><br/>

<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">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="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> </span>)</span> <a href="matrix_3.html#K6" title="MATRIX_3:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K1" title="MATRIXR1:func.1">MXR2MXF</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrixr1.html#D7" target="_self" title="MATRIXR1:def.7">Def7</a></i>
<br/>.= 
 <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="txt" href="matrixr1.html#E1:47"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="matrix_5.html#T40" title="MATRIX_5:th.40">MATRIX_5:40</a></i>
;<br/>
<b>hence </b><a NAME="E3:47"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="matrixr1.html#K7" title="MATRIXR1:func.7">*</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr1.html#K8" title="MATRIXR1:func.8">0_Rmatrix</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c1">A</font></span>)</span>
 ; <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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