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<b>let </b><font color="Maroon">k</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">q</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E1:53"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4" target="_self">dom</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:53"/><b>then </b>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K7" target="_self">^</a> <font color="Maroon">q</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:53"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" target="_self">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K7" target="_self">^</a> <font color="Maroon">q</font></span>)</span>
 ;<br/>


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