<?xml version="1.0"?>
<div class="add">

<b>consider </b><font color="Maroon">F1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="pcomps_1.html#K1">bool</a> <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:55_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font> holds <br/><font color="Maroon">F1</font> <a href="prob_3.html#K7" target="_self">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">F1</font>
;<br/>

<a NAME="E3:55_1_1"/>
for <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font> holds <br/><font color="Maroon">F1</font> <a href="prob_3.html#K7" target="_self">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Si</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:55_1_1_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font>
 ;<br/>

<a NAME="E2:55_1_1_1"/><b>then </b>
<font color="Maroon">F1</font> <a href="prob_3.html#K7" target="_self">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="prob_3.html#E1"><i><font color="Green">Lemma47</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:55_1_1_1"/>
<font color="Maroon">F1</font> <a href="prob_3.html#K7" target="_self">.</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Si</font>
 <b>by </b><i><a class="ref" href="prob_1.html#T43">PROB_1:43</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:55_1_1"/>
for <font color="Olive">k</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font> holds <br/><font color="Maroon">F1</font> <a href="prob_3.html#K7" target="_self">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Si</font>
 ;<br/>


</div>
