<?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">S</font> =  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>;<br/>
<b>thus </b><a NAME="E1:28"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p3">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><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="E1:28_1"/><i><font color="Green">E12</font></i>: 
<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">M</font></span>)</span> <a href="relat_1.html#K5">*</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="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p3">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span> = 
<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#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</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>
<b>by </b><i/>
<br/>.= 
<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#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <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#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <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#K7">|</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="ff_siec.html#D4" target="_self">Def4</a>, </i>
;<br/>
<b>hence </b><a NAME="E3:28_1"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p3">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>


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

<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="E2:28"/><i><font color="Green">E16</font></i>: 
<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">M</font></span>)</span> <a href="relat_1.html#K5">*</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="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p3">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</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>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<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></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<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></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="ff_siec.html#D4" target="_self">Def4</a>, </i>
;<br/>
<b>hence </b><a NAME="E4:28"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">M</font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">M</font></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K6">id</a> <span class="p3">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>


</div>
