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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:8_1"/>
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">n</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="8_1_1"><b>suppose </b></a><a NAME="E1:8_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:8_1_1"/><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#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="matrix_1.html#D3">MATRIX_1:def 3</a></i>;<br/><a NAME="E3:8_1_1"/><b>then </b><i><font color="Green">E31</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>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</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="E4:8_1_1"/>
<span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<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>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="matrix_3.html#T6">MATRIX_3:6</a></i>;<br/><b>hence </b><a NAME="E5:8_1_1"/>
 <a href="matrix_3.html#K2">-</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="8_1_2"><b>suppose </b></a><a NAME="E1:8_1_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:8_1_2"/><b>then </b><i><font color="Green">E36</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>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="finseq_2.html#T69">FINSEQ_2:69</a></i>;<br/><a NAME="E3:8_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K2">-</a> <span class="p2">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="matrix_3.html#D2">MATRIX_3:def 2</a></i>;<br/><b>hence </b><a NAME="E4:8_1_2"/>
 <a href="matrix_3.html#K2">-</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_3.html#K1">0.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>,<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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