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

<b>let </b><font color="Maroon" title="c1">W1</font>, <font color="Maroon" title="c2">W2</font> be   <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E6">A1</font></i>: 
for <font color="Olive" title="b1">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W1</font> iff <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font> )
 ;<br/>

<b>thus </b><a NAME="E2:6"/>
<font color="Maroon" title="c1">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">W2</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">x</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">W1</font> ;<br/>
<a NAME="E3:6_1"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font>
 
<b>by </b><i><a class="txt" href="trees_2.html#E1:6"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:6_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font>
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:6"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">x</font> as    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c2">W2</font> ;<br/>
<a NAME="E5:6"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W1</font>
 
<b>by </b><i><a class="txt" href="trees_2.html#E1:6"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W1</font>
 ;<br/>


</div>
