<?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/>

<a NAME="E1:26"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:26_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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#U2">Transitions</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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:26_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</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#U2">Transitions</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="relat_1.html#K1">dom</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">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>;<br/>
<a NAME="E4:26_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E5:26_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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="relat_1.html#T71">RELAT_1:71</a>, <a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<a NAME="E6:26_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:26_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:26"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:26_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:26_2"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</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#U2">Transitions</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="relat_1.html#K2">rng</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">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E4:26_2"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:26_2_1"/><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></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">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>
 <b>by </b><i><a class="ref" href="relat_1.html#D5">RELAT_1:def 5</a></i>;<br/>
<a NAME="E4:26_2_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="ff_siec.html#E3:26_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E5:26_2_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E6:26_2_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:26_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:26_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_2_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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>
 ;<br/>

<a NAME="E2:26_2_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E3:26_2_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:26_2_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:26_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ff_siec.html#E3:26_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ff_siec.html#E4:26_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:26"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:26_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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#U2">Transitions</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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:26_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</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#U2">Transitions</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="relat_1.html#K1">dom</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">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T13">RELAT_1:13</a></i>;<br/>
<a NAME="E4:26_3"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E5:26_3"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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="relat_1.html#T71">RELAT_1:71</a>, <a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<a NAME="E6:26_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:26_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:26"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:26_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</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#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:26_4"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</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#U2">Transitions</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="relat_1.html#K2">rng</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">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E4:26_4"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_4_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:26_4_1"/><i><font color="Green">E18</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></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">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>
 <b>by </b><i><a class="ref" href="relat_1.html#D5">RELAT_1:def 5</a></i>;<br/>
<a NAME="E4:26_4_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  )
 
<b>by </b><i><a class="txt" href="ff_siec.html#E3:26_4_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="relat_1.html#D11">RELAT_1:def 11</a></i>;<br/>
<a NAME="E5:26_4_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/>
<a NAME="E6:26_4_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E7:26_4_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:26_4_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:26_4"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_4_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_4_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</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>
 ;<br/>

<a NAME="E2:26_4_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</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="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E3:26_4_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="net_1.html#U1">Places</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</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="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:26_4_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:26_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="ff_siec.html#E3:26_4"><i><font color="Green">E16</font></i></a>, <a class="txt" href="ff_siec.html#E4:26_4"><i><font color="Green">E17</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:26"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K9" target="_self">f_exit</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="ff_siec.html#K8" target="_self">f_enter</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <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="txt" href="ff_siec.html#E1:26"><i><font color="Green">E13</font></i></a>, <a class="txt" href="ff_siec.html#E2:26"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ff_siec.html#E3:26"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div>
