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

<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">H</font> be    <a href="seqfunc.html#M1" target="_self">Functional_Sequence</a> of <font color="Maroon">D</font>, <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:49"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">X</font> <a href="seqfunc.html#R1" target="_self">common_on_dom</a> <font color="Maroon">H</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>

<b>assume </b><a NAME="E2:49"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:49"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="seqfunc.html#R1" target="_self">common_on_dom</a> <font color="Maroon">H</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:49"/>
( <span class="p1">(<span class="default"><a href="seqfunc.html#K5" target="_self">abs</a> <font color="Maroon">H</font></span>)</span> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="seq_1.html#K22">abs</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="seqfunc.html#K4" target="_self">-</a> <font color="Maroon">H</font></span>)</span> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="seq_1.html#K17">-</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> )
 <b>by </b><i><a class="txt" href="seqfunc.html#E1:49"><i><font color="Green">E30</font></i></a></i>;<br/>


</div>
