<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="net_1.html#NM1" title="NET_1:NM.1">Pnet</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ff_siec.html#K9" title="FF_SIEC:func.9">f_prox</a> <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;  <a href="ff_siec.html#K10" title="FF_SIEC:func.10">f_flow</a> <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> )</span><br/>

<a NAME="E1:37"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
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#K7" title="RELAT_1:func.7">|</a> 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> the <a href="net_1.html#U3" title="NET_1:sel.3">Flow</a> of <font color="Maroon" title="c1">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E2:37"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ff_siec.html#T13" target="_self" title="FF_SIEC:th.13">Th13</a></span>;<br/>
<a NAME="E3:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A2</font></span>: 
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#K7" title="RELAT_1:func.7">|</a> 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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E4:37"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<span class="p1">(<span class="default">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> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> 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> 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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></span>;<br/>
<a NAME="E5:37"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ff_siec.html#T13" target="_self" title="FF_SIEC:th.13">Th13</a></span>;<br/>
<a NAME="E6:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<span class="p1">(<span class="default">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> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> 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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E7:37"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E8:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<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#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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></span>;<br/>
<a NAME="E9:37"/>
 <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> 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> <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#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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T28" title="RELSET_1:th.28">RELSET_1:28</a></span>;<br/>
<a NAME="E10:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> 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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E11:37"/>
<span class="p1">(<span class="default">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#K7" title="RELAT_1:func.7">|</a> the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">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> </span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="net_1.html#U1" title="NET_1:sel.1">Places</a> of <font color="Maroon" title="c1">M</font></span>)</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:37"/>
 <a href="ff_siec.html#K9" title="FF_SIEC:func.9">f_prox</a> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ff_siec.html#K10" title="FF_SIEC:func.10">f_flow</a> <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></span><br/>

<a NAME="E13:37"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ff_siec.html#T13" target="_self" title="FF_SIEC:th.13">Th13</a></span>;<br/>
<a NAME="E14:37"/>
 <a href="relat_1.html#K6" title="RELAT_1:func.6">id</a> <span class="p1">(<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> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T28" title="RELSET_1:th.28">RELSET_1:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:37"/>
 <a href="ff_siec.html#K10" title="FF_SIEC:func.10">f_flow</a> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:37"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
