<?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>set </b><font color="Maroon">c<sub>2</sub></font> = 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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:37"/><i><font color="Green">E13</font></i>: 
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<a NAME="E1:37_1"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E2:37_1"/><i><font color="Green">E15</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#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E3:37_1"/><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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sysrel.html#T29">SYSREL:29</a></i>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <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#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ff_siec.html#E1:37_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ff_siec.html#E2:37_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ff_siec.html#E3:37_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="ff_siec.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E5:37_1"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:37"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:37_2"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E2:37_2"/><i><font color="Green">E16</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#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E3:37_2"/><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sysrel.html#T29">SYSREL:29</a></i>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <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#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ff_siec.html#E1:37_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ff_siec.html#E2:37_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ff_siec.html#E3:37_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="ff_siec.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E5:37_2"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:37"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_3"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:37_3"/><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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E2:37_3"/><i><font color="Green">E17</font></i>: 
<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E3:37_3"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sysrel.html#T29">SYSREL:29</a></i>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ff_siec.html#E1:37_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ff_siec.html#E2:37_3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ff_siec.html#E3:37_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="ff_siec.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E5:37_3"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:37"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_4"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:37_4"/><i><font color="Green">E16</font></i>: 
<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E2:37_4"/><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="ff_siec.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E3:37_4"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sysrel.html#T29">SYSREL:29</a></i>;<br/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>

<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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sysrel.html#T20">SYSREL:20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p3">(<span class="default"><a href="relat_1.html#K6">id</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T51">RELAT_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</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">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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ff_siec.html#E1:37_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ff_siec.html#E2:37_4"><i><font color="Green">E17</font></i></a>, <a class="txt" href="ff_siec.html#E3:37_4"><i><font color="Green">E18</font></i></a>, <a class="ref" href="ff_siec.html#T16" target="_self">Th16</a></i>
<br/>.= 
 <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E5:37_4"/>
<span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:37"/>
( <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K17" target="_self">f_escape</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ff_siec.html#K16" target="_self">f_entrance</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="ff_siec.html#E1:37"><i><font color="Green">E13</font></i></a>, <a class="txt" href="ff_siec.html#E2:37"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ff_siec.html#E3:37"><i><font color="Green">E15</font></i></a></i>;<br/>


</div>
