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<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM4">Matrix</a> of <font color="Maroon">K</font>;<br/>



<a NAME="E1:49"/><i><font color="Green">E30</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/>
<a NAME="E2:49"/><i><font color="Green">E31</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D3">MATRIX_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> 0 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1"><b>suppose </b></a><a NAME="E1:49_1_1"/><i><font color="Green">E29</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:49_1_1"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/><a NAME="E3:49_1_1"/><i><font color="Green">E33</font></i>: 
 <a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font> is   <a href="matrix_1.html#NM6">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>, <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font>,<font color="Maroon">K</font>
 <b>by </b><i>, , <a class="ref" href="matrix_1.html#T20">MATRIX_1:20</a></i>;<br/><a NAME="E4:49_1_1"/>
<span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font></span>)</span> <a href="matrix_3.html#K3">+</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="matrix_3.html#T4">MATRIX_3:4</a></i>;<br/><b>hence </b><a NAME="E5:49_1_1"/>
<span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="matrix_4.html#T1" target="_self">Th1</a>, <a class="ref" href="matrix_3.html#T6">MATRIX_3:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2"><b>suppose </b></a><a NAME="E1:49_1_2"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:49_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p3">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">M</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="matrix_3.html#D3">MATRIX_3:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_1_2"/>
<span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="matrix_4.html#K1" target="_self">-</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="matrix_3.html#K2">-</a> <font color="Maroon">M</font>
 <b>by </b><i>, , , <a class="ref" href="matrix_1.html#T37">MATRIX_1:37</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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