<?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>  holds <br/>(  not  <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>  or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="net_1.html#K2" title="NET_1:func.2">Pre</a> <font color="Maroon" title="c1">N</font>,<font color="Olive" title="b1">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"> (  not  <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>  or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="net_1.html#K2" title="NET_1:func.2">Pre</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> )</span><br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E14">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="net_1.html#K2" title="NET_1:func.2">Pre</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E2:23"/><b>then </b>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">N</font> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">N</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:23"/>
(  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or  <a href="net_1.html#K4" title="NET_1:func.4">enter</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="net_1.html#K2" title="NET_1:func.2">Pre</a> <font color="Maroon" title="c1">N</font>,<font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="txt" href="net_1.html#E1:23"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="net_1.html#D9" target="_self" title="NET_1:def.9">Def9</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>
