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<b>let </b><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>reconsider </b><font color="Maroon" title="c3">M</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#T29" title="FINSEQ_1:th.29">FINSEQ_1:29</a></i>;<br/>
<a NAME="E2:21"/>
<font color="Maroon" title="c3">M</font> is <a href="matrix_1.html#V1" title="MATRIX_1:attr.1">tabular</a>
 
<b>by </b><i><a class="ref" href="matrix_1.html#T5" target="_self" title="MATRIX_1:th.5">Th5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">M</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <font color="Maroon" title="c2">D</font> ;<br/>
<a NAME="E4:21"/>
<font color="Maroon" title="c4">M</font> is    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of 0,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:21_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="matrix_1.html#D3" target="_self" title="MATRIX_1:def.3">MATRIX_1:def 3</a><br/>

<b>let </b><font color="Maroon" title="c5">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">D</font>;<br/>

<b>assume </b><a NAME="E2:21_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">M</font>
 ;<br/>

<b>hence </b><a NAME="E3:21_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T27" title="FINSEQ_1:th.27">FINSEQ_1:27</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:21"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is    <a href="matrix_1.html#M1" title="MATRIX_1:mode.1">Matrix</a> of 0,<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">D</font>
 ;<br/>


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