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

<a NAME="E1:14"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<a NAME="E1:14_1"/><i><font color="Green">E12</font></i>: 
the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:14_1"/><i><font color="Green">E16</font></i>: 
the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a>  <a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E3:14_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E4:14_1"/>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E5:14_1"/><b>then </b><i><font color="Green">E18</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E6:14_1"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="net_1.html#U2">Transitions</a> of <font color="Maroon">M</font>,the <a href="net_1.html#U1">Places</a> of <font color="Maroon">M</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="net_1.html#D1">NET_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:14_1"/>
the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:14"/>
( the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="net_1.html#U3">Flow</a> of <font color="Maroon">M</font> <a href="relat_1.html#K4">~</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1">Elements</a> <font color="Maroon">M</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="sysrel.html#T16">SYSREL:16</a></i>;<br/>


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