<?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">H1</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">H2</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="E1:48"/><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">H1</font> &amp; <font color="Maroon">X</font> <a href="seqfunc.html#R1" target="_self">common_on_dom</a> <font color="Maroon">H2</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="E2:48"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:48"/><b>then </b><i><font color="Green">E41</font></i>: 
<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">H1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:48"/>
<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">H2</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:48"/>
( <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K6" target="_self">+</a> <font color="Maroon">H2</font></span>)</span> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K7" target="_self">-</a> <font color="Maroon">H2</font></span>)</span> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="seqfunc.html#K8" target="_self">(#)</a> <font color="Maroon">H2</font></span>)</span> <a href="seqfunc.html#K10" target="_self">#</a> <font color="Maroon">x</font> )
 <b>by </b><i>, <a class="ref" href="seqfunc.html#D1" target="_self">Def1</a></i>;<br/>


</div>
