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<b>consider </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/>
<b>reconsider </b><font color="Maroon">Z</font> = <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="finseq_2.html#K3">*</a> </span>)</span> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">Z</font> <a href="rfunct_3.html#K5">--&gt;</a> <font color="Maroon">y</font> as   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font> <a href="finseq_2.html#K3">*</a> ,<font color="Maroon">Y</font> ;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<a NAME="E4:34_1_1"/><i><font color="Green">E48</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<b>thus </b><a NAME="E5:34_1_1"/>
not <font color="Maroon">f</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">y</font> be   <a href="finseq_1.html#NM1">FinSequence</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D4" target="_self">COMPUT_1:def 4</a><br/>

<b>assume </b><a NAME="E6:34_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> )
 ;<br/>

<a NAME="E7:34_1_1"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<b>hence </b><a NAME="E8:34_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font>
 ;<br/>


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