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<a NAME="E1:69_1_1"/><i><font color="Green">E48</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:69_1_1"/>
<font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> is <a href="comput_1.html#V3" target="_self">len-total</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="comput_1.html#D3" target="_self">COMPUT_1:def 3</a><br/>

<b>assume </b><a NAME="E1:69_1_1_1"/><i><font color="Green">E49</font></i>: 
(  <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> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font></span>)</span> )
 ;<br/>

<a NAME="E2:69_1_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>
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:69_1_1_1"/><b>then </b>
<font color="Maroon">y</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<b>hence </b><a NAME="E4:69_1_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:69_1_1"/>
( <font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> is <a href="comput_1.html#V3" target="_self">len-total</a> &amp; not <font color="Maroon">n</font> <a href="comput_1.html#K7" target="_self">succ</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a> )
 <b>by </b><i>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>


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