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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D</font>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E49</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/>

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>thus </b><a NAME="E2:29"/>
( <font color="Maroon">M</font> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>,<font color="Maroon">n</font>,<font color="Maroon">D</font> implies <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1" target="_self">width</a> <font color="Maroon">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:29_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">M</font> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>,<font color="Maroon">n</font>,<font color="Maroon">D</font>
 ;<br/>

<b>consider </b><font color="Maroon">s</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E3:29_1"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1" target="_self">width</a> <font color="Maroon">M</font> )
 <b>by </b><i>, </i>;<br/>
<a NAME="E4:29_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">q</font> = <font color="Maroon">s</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font> <b>by </b><i>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E6:29_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E7:29_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1" target="_self">width</a> <font color="Maroon">M</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:29"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1" target="_self">width</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E4:29"/><b>then </b>
for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>  st <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> holds <br/> <a href="finseq_1.html#K3">len</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:29"/>
<font color="Maroon">M</font> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font>,<font color="Maroon">n</font>,<font color="Maroon">D</font>
 <b>by </b><i/>;<br/>


</div>
