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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">p</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>



<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E2:19"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">p'</font></span><a href="finseq_1.html#K12">*&gt;</a></span> is <a href="matrix_1.html#V1" target="_self">tabular</a>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">M</font> = <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K9">*&gt;</a></span> as   <a href="matrix_1.html#NM1">Matrix</a> of <font color="Maroon">D</font> ;<br/>
<a NAME="E4:19"/>
<font color="Maroon">M</font> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of 1, <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>,<font color="Maroon">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:19_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="matrix_1.html#D3" target="_self">MATRIX_1:def 3</a><br/>

<b>let </b><font color="Maroon">q</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>

<b>assume </b><a NAME="E2:19_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E3:19_1"/><b>then </b>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">p</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:19"/>
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">p</font></span><a href="finseq_1.html#K9">*&gt;</a></span> is    <a href="matrix_1.html#M1" target="_self">Matrix</a> of 1, <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>,<font color="Maroon">D</font>
 ;<br/>


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