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<div class="add">

<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="net_1.html#NM1" title="NET_1:NM.1">Pnet</a>;<br/>

<a NAME="E1:12"/>
the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_1"/><i><font color="Green" title="E4">A1</font></i>: 
the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:12_1"/><i><font color="Green" title="E5">A2</font></i>: 
the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E3:12_1"/><b>then </b><i><font color="Green" title="E6">A3</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E1:12_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E4:12_1"/>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E1:12_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="ff_siec.html#E2:12_1"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E5:12_1"/><b>then </b><i><font color="Green" title="E7">A4</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="ff_siec.html#E3:12_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E6:12_1"/>
the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="net_1.html#U2" title="NET_1:sel.2">Transitions</a> of <font color="Maroon" title="c1">M</font>,the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="net_1.html#D1" title="NET_1:def.1">NET_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:12_1"/>
the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="ff_siec.html#E5:12_1"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:12"/>
( the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span>,<span class="p2">(<span class="default"><a href="net_1.html#K1" title="NET_1:func.1">Elements</a> <font color="Maroon" title="c1">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <b>by </b><i><a class="ref" href="sysrel.html#T16" title="SYSREL:th.16">SYSREL:16</a></i>;<br/>


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