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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</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> ;<br/><b>let </b><font color="Maroon" title="c4">B</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c5">A</font> be    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">k</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>









<b>assume </b><a NAME="E1:64"/><i><font color="Green" title="E45">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> 
 ;<br/>

<b>let </b><font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c7">j</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> ;<br/>



<b>assume </b><a NAME="E2:64"/><i><font color="Green" title="E46">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span>
 ;<br/>

<a NAME="E3:64"/><b>then </b><i><font color="Green" title="E47">A3</font></i>: 
( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span> &amp; <font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E4:64"/><i><font color="Green" title="E48">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></i>;<br/>
<a NAME="E5:64"/><i><font color="Green" title="E49">A5</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E1:64"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green" title="E50">A6</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">B</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="c5">A</font>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E1:64"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="matrixr2.html#E4:64"><i><font color="Green" title="E48">A4</font></i></a>, <a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></i>;<br/>
<a NAME="E7:64"/><i><font color="Green" title="E51">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c6">i</font></span>)</span> <a href="matrprob.html#NK7" title="MATRPROB:NK.7">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c5">A</font>,<font color="Maroon" title="c7">j</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E2:64"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="matrixr2.html#E6:64"><i><font color="Green" title="E50">A6</font></i></a>, <a class="ref" href="matrprob.html#T39" title="MATRPROB:th.39">MATRPROB:39</a></i>;<br/>
<a NAME="E8:64"/><i><font color="Green" title="E52">A8</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c6">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E4:64"><i><font color="Green" title="E48">A4</font></i></a>, <a class="txt" href="matrixr2.html#E5:64"><i><font color="Green" title="E49">A5</font></i></a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>;<br/>
<a NAME="E9:64"/>
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E4:64"><i><font color="Green" title="E48">A4</font></i></a>, <a class="txt" href="matrixr2.html#E5:64"><i><font color="Green" title="E49">A5</font></i></a>, <a class="ref" href="matrprob.html#T39" title="MATRPROB:th.39">MATRPROB:39</a></i>;<br/>
<a NAME="E10:64"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c6">i</font></span>)</span> <a href="matrixr1.html#K12" title="MATRIXR1:func.12">*</a> <font color="Maroon" title="c5">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="matrixr2.html#E3:64"><i><font color="Green" title="E47">A3</font></i></a>, <a class="txt" href="matrixr2.html#E8:64"><i><font color="Green" title="E52">A8</font></i></a>, <a class="ref" href="matrixr1.html#T62" title="MATRIXR1:th.62">MATRIXR1:62</a></i>;<br/>
<b>hence </b><a NAME="E11:64"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c6">i</font></span>)</span> <a href="matrixr1.html#K12" title="MATRIXR1:func.12">*</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="matrixr2.html#E7:64"><i><font color="Green" title="E51">A7</font></i></a>, <a class="txt" href="matrixr2.html#E8:64"><i><font color="Green" title="E52">A8</font></i></a>, <a class="ref" href="matrprob.html#T40" title="MATRPROB:th.40">MATRPROB:40</a></i>;<br/>


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