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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">i</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">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<a NAME="E1:5"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">q</font> where <font color="Olive">q</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:5_1"/><b>then </b>
 ex <font color="Olive">q</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:5_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:5"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font>
 ;<br/>

<b>assume </b><a NAME="E4:5"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E5:5"/><b>then </b>
<font color="Maroon">p</font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E6:5"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</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/>
<b>hence </b><a NAME="E7:5"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">i</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/>


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