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

<b>let </b><font color="Maroon">M</font> be   <a href="net_1.html#NM1">Pnet</a>;<br/>

<b>set </b><font color="Maroon">T</font> =  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>;<br/>
<b>thus </b><a NAME="E1:20"/>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">R</font> = <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font>;<br/>
<a NAME="E1:20_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   holds not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:20_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:20_1_1"/><b>then </b><i><font color="Green">E12</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:20_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a>  )
 
<b>by </b><i><a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E4:20_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E5:20_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:20_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T56">RELAT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1"/>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


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

<b>thus </b><a NAME="E2:20"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">R</font> = the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font>;<br/>
<a NAME="E1:20_2"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   holds not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:20_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:20_2_1"/><b>then </b><i><font color="Green">E16</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:20_2_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E4:20_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:20_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_2"/><b>then </b>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T56">RELAT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:20_2"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


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

<b>thus </b><a NAME="E3:20"/>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">R</font> = <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>;<br/>
<a NAME="E1:20_3"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   holds not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:20_3_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:20_3_1"/><b>then </b><i><font color="Green">E17</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:20_3_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a>  )
 
<b>by </b><i><a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E4:20_3_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E5:20_3_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:20_3_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T56">RELAT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:20_3"/>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


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

<b>set </b><font color="Maroon">R</font> = the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>;<br/>
<a NAME="E4:20"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   holds not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:20_4"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:20_4"/><b>then </b><i><font color="Green">E18</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:20_4"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E4:20_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:20_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:20"/><b>then </b>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T56">RELAT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E6:20"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>


</div>
