<?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>thus </b><a NAME="E1:25"/>
 <a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<a NAME="E1:25_1"/><i><font color="Green">E13</font></i>: 
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:25_1_1"/>
the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:25_1_1"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</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">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="sysrel.html#T33">SYSREL:33</a></i>;<br/>
<a NAME="E3:25_1_1"/>
 <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">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="relset_1.html#T28">RELSET_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:25_1_1"/>
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="txt" href="ff_siec.html#E2:25_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:25_1"/><i><font color="Green">E14</font></i>: 
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>
<a NAME="E3:25_1"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E4:25_1"/><b>then </b>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E2:25_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:25_1"/><b>then </b>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E1:25_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E6:25_1"/>
 <a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>


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

<a NAME="E2:25"/><i><font color="Green">E13</font></i>: 
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

<a NAME="E1:25_2"/>
the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:25_2"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</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">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="sysrel.html#T33">SYSREL:33</a></i>;<br/>
<a NAME="E3:25_2"/>
 <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">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="relset_1.html#T28">RELSET_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:25_2"/>
 <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="txt" href="ff_siec.html#E2:25_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:25"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>
<a NAME="E4:25"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
<span class="p1">(<span class="default">the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E3:25"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:25"/><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">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E2:25"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E7:25"/>
 <a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>


</div>
