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

<b>let </b><font color="Maroon" title="c1">CPNT1</font>, <font color="Maroon" title="c2">CPNT2</font> be    <a href="petri_2.html#L1" title="PETRI_2:struct.1">Colored_PT_net_Str</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t1</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font><br/> for <font color="Olive" title="b2">t2</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font>  st the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; <font color="Olive" title="b1">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t2</font> holds <br/>(  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  )</span><br/><b>let </b><font color="Maroon" title="c3">t1</font> be   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t2</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font>  st the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; <font color="Maroon" title="c3">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> holds <br/>(  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  )</span><br/><b>let </b><font color="Maroon" title="c4">t2</font> be   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; <font color="Maroon" title="c3">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t2</font> implies (  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  ) )</span><br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E14">AS1</font></i>: 
( the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; <font color="Maroon" title="c3">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  )</span><br/>

<b>thus </b><a NAME="E2:21"/>
 <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/>

<b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c6">s</font> being   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c1">CPNT1</font><b> such that </b><br/><a NAME="E3:21_1"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> &amp;  ex <font color="Olive" title="b1">f</font> being  <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <font color="Maroon" title="c1">CPNT1</font> ex <font color="Olive" title="b2">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> st <br/>( <font color="Olive" title="b2">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Olive" title="b2">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> ) )
 ;<br/>
<b>consider </b><font color="Maroon" title="c7">f</font> being   <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <font color="Maroon" title="c1">CPNT1</font>, <font color="Maroon" title="c8">w</font> being   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font><b> such that </b><br/><a NAME="E5:21_1"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c8">w</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a>, <a class="txt" href="#E3:21_1"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<a NAME="E6:21_1"/><i><font color="Green" title="E17">P1</font></i>: 
<font color="Maroon" title="c7">f</font> is   <a href="petri.html#NM6" title="PETRI:NM.6">S-T_arc</a> of <font color="Maroon" title="c2">CPNT2</font>
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E7:21_1"/>
<font color="Maroon" title="c5">x</font> is   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c2">CPNT2</font>
 
<b>by </b><i><a class="txt" href="#E3:21_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:21_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="#E6:21_1"><i><font color="Green" title="E17">P1</font></i></a>, <a class="txt" href="#E5:21_1"><i><font color="Green" title="E16">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a>  )</span><br/>

<b>assume </b><a NAME="E3:21"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c6">s</font> being   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c1">CPNT1</font><b> such that </b><br/><a NAME="E5:21"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font> &amp;  ex <font color="Olive" title="b1">f</font> being  <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <font color="Maroon" title="c1">CPNT1</font> ex <font color="Olive" title="b2">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> st <br/>( <font color="Olive" title="b2">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">w</font>,<font color="Maroon" title="c6">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> ) )
 ;<br/>
<b>consider </b><font color="Maroon" title="c7">f</font> being   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <font color="Maroon" title="c1">CPNT1</font>, <font color="Maroon" title="c8">w</font> being   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font><b> such that </b><br/><a NAME="E7:21"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c5">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a></i>;<br/>
<a NAME="E8:21"/><i><font color="Green" title="E17">P1</font></i>: 
<font color="Maroon" title="c7">f</font> is   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <font color="Maroon" title="c2">CPNT2</font>
 
<b>by </b><i><a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E9:21"/>
<font color="Maroon" title="c5">x</font> is   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c2">CPNT2</font>
 
<b>by </b><i><a class="txt" href="#E5:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E1:21"><i><font color="Green" title="E14">AS1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:21"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">t2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="petri.html#K8" title="PETRI:func.8">*'</a> 
 <b>by </b><i><a class="txt" href="#E8:21"><i><font color="Green" title="E17">P1</font></i></a>, <a class="txt" href="#E7:21"><i><font color="Green" title="E16">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
