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

<b>let </b><font color="Maroon" title="c1">N</font> be   <a href="net_1.html#NM1" title="NET_1:NM.1">Pnet</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">X</font> holds <br/> <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K10" title="NET_1:func.10">Ext</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b2">X</font></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/> <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K10" title="NET_1:func.10">Ext</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b1">X</font></span><br/><b>let </b><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> implies  <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K10" title="NET_1:func.10">Ext</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c3">X</font> )</span><br/>





<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E22">A1</font></i>: 
(  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K10" title="NET_1:func.10">Ext</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c3">X</font></span><br/>

<a NAME="E2:32"/><b>then </b>
 <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">N</font>
 
<b>by </b><i><a class="ref" href="net_1.html#T26" target="_self" title="NET_1:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
 <a href="net_1.html#K5" title="NET_1:func.5">exit</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="net_1.html#K10" title="NET_1:func.10">Ext</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="net_1.html#E1:32"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="net_1.html#D15" target="_self" title="NET_1:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
