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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="net_1.html#NM1">Pnet</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E21</font></i>: 
 <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green">E22</font></i>: 
(  <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> or  <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="net_1.html#K3" target="_self">Post</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="net_1.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E3:27"/>
(  <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> implies  <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:27_1"/><i><font color="Green">E23</font></i>: 
 <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E2:27_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="net_1.html#E1:27"><i><font color="Green">E21</font></i></a></i>;<br/>
<a NAME="E3:27_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:27_1"/>
 <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="net_1.html#E1:27_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:27"/>
 <a href="net_1.html#K5" target="_self">exit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1" target="_self">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="net_1.html#E2:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="net_1.html#T18" target="_self">Th18</a></i>;<br/>


</div>
