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<b>consider </b><font color="Maroon" title="c5">q12</font>, <font color="Maroon" title="c6">q21</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>, <font color="Maroon" title="c7">O12</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font>, <font color="Maroon" title="c8">O21</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font><b> such that </b><br/><a NAME="E2:29_1_1"/><i><font color="Green" title="E20">P1</font></i>: 
( <font color="Maroon" title="c3">O</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="c7">O12</font>,<font color="Maroon" title="c8">O21</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font> &amp; ( for <font color="Olive" title="b1">t01</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font>  st <font color="Olive" title="b1">t01</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> holds <br/><font color="Maroon" title="c5">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Olive" title="b1">t01</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">t02</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font>  st <font color="Olive" title="b1">t02</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> holds <br/><font color="Maroon" title="c6">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Olive" title="b1">t02</font></span>)</span> ) &amp; <font color="Maroon" title="c4">q</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">q12</font>,<font color="Maroon" title="c6">q21</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="ref" href="petri_2.html#D13" target="_self" title="PETRI_2:def.13">Def9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">P12</font> = the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">T12</font> = the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E5:29_1_1"/>
( 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> <font color="Maroon" title="c9">P12</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> <font color="Maroon" title="c10">T12</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">E1</font> = the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font> <b>by </b><i><a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<a NAME="E7:29_1_1"/>
( the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">P12</font> &amp; the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">T12</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">E2</font> = the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font> <b>by </b><i><a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<a NAME="E9:29_1_1"/>
<font color="Maroon" title="c11">E1</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c12">E2</font> is    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c13">ST12</font> = the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font> ;<br/>
<a NAME="E11:29_1_1"/>
( 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> <font color="Maroon" title="c10">T12</font> &amp; 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> <font color="Maroon" title="c9">P12</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c14">E21</font> = the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> <b>by </b><i><a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<a NAME="E13:29_1_1"/>
( the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">T12</font> &amp; the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">P12</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c15">E22</font> = the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> <b>by </b><i><a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<a NAME="E15:29_1_1"/>
<font color="Maroon" title="c14">E21</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c15">E22</font> is    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c16">TTS12</font> = the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> ;<br/>
<a NAME="E17:29_1_1"/>
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> <font color="Maroon" title="c10">T12</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="E18:29_1_1"/><b>then </b><i><font color="Green" title="E21">L30</font></i>: 
 <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">T12</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E19:29_1_1"/>
the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">T12</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="E20:29_1_1"/><b>then </b><i><font color="Green" title="E22">L31</font></i>: 
 <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">T12</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E21:29_1_1"/><i><font color="Green" title="E23">L32</font></i>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">P12</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="E22:29_1_1"/><i><font color="Green" title="E24">L33</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> <font color="Maroon" title="c9">P12</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">E31</font> = <font color="Maroon" title="c7">O12</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> <b>by </b><i><a class="txt" href="#E18:29_1_1"><i><font color="Green" title="E21">L30</font></i></a>, <a class="txt" href="#E21:29_1_1"><i><font color="Green" title="E23">L32</font></i></a>, <a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">E32</font> = <font color="Maroon" title="c8">O21</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> <b>by </b><i><a class="txt" href="#E20:29_1_1"><i><font color="Green" title="E22">L31</font></i></a>, <a class="txt" href="#E22:29_1_1"><i><font color="Green" title="E24">L33</font></i></a>, <a class="ref" href="relset_1.html#T17" title="RELSET_1:th.17">RELSET_1:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c19">TS12</font> = <font color="Maroon" title="c16">TTS12</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c9">P12</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c20">CS12</font> = the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>set </b><font color="Maroon" title="c21">CR12</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font>;<br/>
<b>set </b><font color="Maroon" title="c22">CPNT12</font> =  <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #);<br/>
<b>set </b><font color="Maroon" title="c23">R1</font> = the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font>;<br/>
<b>set </b><font color="Maroon" title="c24">R2</font> = the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font>;<br/>
<b>set </b><font color="Maroon" title="c25">R3</font> = <font color="Maroon" title="c5">q12</font>;<br/>
<b>set </b><font color="Maroon" title="c26">R4</font> = <font color="Maroon" title="c6">q21</font>;<br/>
<a NAME="E27:29_1_1"/><i><font color="Green" title="E25">P2</font></i>: 
<font color="Maroon" title="c19">TS12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">O12</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c8">O21</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/>
<div><i><font color="Green" title="E26">P22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c27">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )</span><br/><b>assume </b><a NAME="E1:29_1_1_1"/>
<font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )</span><br/><a NAME="E2:29_1_1_1"/><b>then </b>
( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 <b>by </b><i><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></i>;<br/><a NAME="E3:29_1_1_1"/><b>then </b>
( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 <b>by </b><i><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></i>;<br/><b>hence </b><a NAME="E4:29_1_1_1"/>
( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 <b>by </b><i><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</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>
<a NAME="E29:29_1_1"/><i><font color="Green" title="E27">LM6T1</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E30:29_1_1"/><i><font color="Green" title="E28">LM6T2</font></i>: 
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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E31:29_1_1"/><i><font color="Green" title="E29">LM6T3</font></i>: 
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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E32:29_1_1"/><i><font color="Green" title="E30">Q2</font></i>: 
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E33:29_1_1"/>
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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</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="E34:29_1_1"/><b>then </b><i><font color="Green" title="E31">LM6T4</font></i>: 
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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="#E32:29_1_1"><i><font color="Green" title="E30">Q2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E35:29_1_1"/><i><font color="Green" title="E32">LM6S1</font></i>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E36:29_1_1"/><i><font color="Green" title="E33">LM6S2</font></i>: 
the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E37:29_1_1"/><i><font color="Green" title="E34">LM6S3</font></i>: 
the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c2">CPNT2</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E38:29_1_1"/><i><font color="Green" title="E35">Q2</font></i>: 
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E39:29_1_1"/>
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</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="E40:29_1_1"/><b>then </b><i><font color="Green" title="E36">LM6S4</font></i>: 
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="#E38:29_1_1"><i><font color="Green" title="E35">Q2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E41:29_1_1"/><i><font color="Green" title="E37">LM7T1</font></i>: 
the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="#E1:29"><i><font color="Green" title="E19">AS</font></i></a>, <a class="ref" href="petri_2.html#D11" target="_self" title="PETRI_2:def.11">Def7A</a></i>;<br/>
<a NAME="E42:29_1_1"/><i><font color="Green" title="E38">LM7T4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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="c1">CPNT1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/>
<a NAME="E43:29_1_1"/><i><font color="Green" title="E39">LM7T5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/>
<a NAME="E44:29_1_1"/><i><font color="Green" title="E40">LM7T</font></i>: 
( <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="petri_2.html#E23"><i><font color="Green" title="E15">LM8</font></i></a>, <a class="txt" href="#E41:29_1_1"><i><font color="Green" title="E37">LM7T1</font></i></a>, <a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="txt" href="#E42:29_1_1"><i><font color="Green" title="E38">LM7T4</font></i></a>, <a class="txt" href="#E43:29_1_1"><i><font color="Green" title="E39">LM7T5</font></i></a></i>;<br/>
<div><i><font color="Green" title="E41">s10</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c27">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> implies <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> )</span><br/><b>assume </b><a NAME="E1:29_1_1_2"/>
<font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font></span><br/><a NAME="E2:29_1_1_2"/><b>then </b><i><font color="Green" title="E42">PP1</font></i>: 
( <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 <b>by </b><i><a class="txt" href="#E28:29_1_1"><i><font color="Green" title="E26">P22</font></i></a></i>;<br/><a NAME="E3:29_1_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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="c1">CPNT1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><a NAME="E4:29_1_1_2"/><b>then </b><i><font color="Green" title="E43">PP2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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="c1">CPNT1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E5:29_1_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><a NAME="E6:29_1_1_2"/><b>then </b><i><font color="Green" title="E44">pp</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</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>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>thus </b><a NAME="E7:29_1_1_2"/>
<font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a>, <a class="txt" href="#E6:29_1_1_2"><i><font color="Green" title="E44">pp</font></i></a>, <a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="txt" href="#E2:29_1_1_2"><i><font color="Green" title="E42">PP1</font></i></a>, <a class="txt" href="#E4:29_1_1_2"><i><font color="Green" title="E43">PP2</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>
<a NAME="E46:29_1_1"/><b>then </b><i><font color="Green" title="E42">S10</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E47:29_1_1"/><i><font color="Green" title="E43">SS1</font></i>: 
for <font color="Olive" title="b1">t</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)  st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) holds <br/> ex <font color="Olive" title="b2">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b3">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b4">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b2">CS</font>,<font color="Olive" title="b3">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b2">CS</font>,<font color="Olive" title="b4">O</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c27">t</font> be   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) implies  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font> )</span><br/>

<b>assume </b><a NAME="E1:29_1_1_3"/><i><font color="Green" title="E44">SS2</font></i>: 
<font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_3_1_1"/>
( <font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 </span><b>by </b><i><a class="txt" href="#E1:29_1_1_3"><i><font color="Green" title="E44">SS2</font></i></a>, <a class="txt" href="#E28:29_1_1"><i><font color="Green" title="E26">P22</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_3_1_1_1"/><i><font color="Green" title="E45">S4</font></i>: 
<font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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">  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font></span><br/><div class="add"><a NAME="E2:29_1_1_3_1_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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="c1">CPNT1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c28">t1</font> = <font color="Maroon" title="c27">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_1"><i><font color="Green" title="E45">S4</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><b>consider </b><font color="Maroon" title="c29">CS1</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>, <font color="Maroon" title="c30">I1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <font color="Maroon" title="c31">O1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">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> </span>)</span><b> such that </b><br/><a NAME="E5:29_1_1_3_1_1_1"/><i><font color="Green" title="E46">T6</font></i>: 
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c28">t1</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS1</font>,<font color="Maroon" title="c30">I1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS1</font>,<font color="Maroon" title="c31">O1</font>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a>, <a class="txt" href="#E1:29_1_1_3_1_1_1"><i><font color="Green" title="E45">S4</font></i></a></i>;<br/><a NAME="E6:29_1_1_3_1_1_1"/>
the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c32">CS</font> = <font color="Maroon" title="c29">CS1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:29_1_1_3_1_1_1"/>
 <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="c28">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="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E29:29_1_1"><i><font color="Green" title="E27">LM6T1</font></i></a>, <a class="txt" href="#E30:29_1_1"><i><font color="Green" title="E28">LM6T2</font></i></a>, <a class="txt" href="#E31:29_1_1"><i><font color="Green" title="E29">LM6T3</font></i></a>, <a class="txt" href="#E34:29_1_1"><i><font color="Green" title="E31">LM6T4</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c33">I</font> = <font color="Maroon" title="c30">I1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E10:29_1_1_3_1_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">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="c27">t</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="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E29:29_1_1"><i><font color="Green" title="E27">LM6T1</font></i></a>, <a class="txt" href="#E30:29_1_1"><i><font color="Green" title="E28">LM6T2</font></i></a>, <a class="txt" href="#E31:29_1_1"><i><font color="Green" title="E29">LM6T3</font></i></a>, <a class="txt" href="#E34:29_1_1"><i><font color="Green" title="E31">LM6T4</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c34">O</font> = <font color="Maroon" title="c31">O1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E12:29_1_1_3_1_1_1"/>
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c32">CS</font>,<font color="Maroon" title="c33">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c32">CS</font>,<font color="Maroon" title="c34">O</font>
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_1"><i><font color="Green" title="E45">S4</font></i></a>, <a class="txt" href="petri_2.html#E22"><i><font color="Green" title="E14">LM7</font></i></a>, <a class="txt" href="#E44:29_1_1"><i><font color="Green" title="E40">LM7T</font></i></a>, <a class="txt" href="#E5:29_1_1_3_1_1_1"><i><font color="Green" title="E46">T6</font></i></a></i>;<br/><b>hence </b><a NAME="E13:29_1_1_3_1_1_1"/>
 ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font>
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_3_1_1_2"/><i><font color="Green" title="E45">S5</font></i>: 
<font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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">  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font></span><br/><div class="add"><a NAME="E2:29_1_1_3_1_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c28">t1</font> = <font color="Maroon" title="c27">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font> <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_2"><i><font color="Green" title="E45">S5</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><b>consider </b><font color="Maroon" title="c29">CS1</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>, <font color="Maroon" title="c30">I1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <font color="Maroon" title="c31">O1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">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> </span>)</span><b> such that </b><br/><a NAME="E5:29_1_1_3_1_1_2"/><i><font color="Green" title="E46">T6</font></i>: 
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c28">t1</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS1</font>,<font color="Maroon" title="c30">I1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS1</font>,<font color="Maroon" title="c31">O1</font>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a>, <a class="txt" href="#E1:29_1_1_3_1_1_2"><i><font color="Green" title="E45">S5</font></i></a></i>;<br/><a NAME="E6:29_1_1_3_1_1_2"/>
the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c32">CS</font> = <font color="Maroon" title="c29">CS1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E8:29_1_1_3_1_1_2"/>
 <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="c28">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="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E35:29_1_1"><i><font color="Green" title="E32">LM6S1</font></i></a>, <a class="txt" href="#E36:29_1_1"><i><font color="Green" title="E33">LM6S2</font></i></a>, <a class="txt" href="#E37:29_1_1"><i><font color="Green" title="E34">LM6S3</font></i></a>, <a class="txt" href="#E40:29_1_1"><i><font color="Green" title="E36">LM6S4</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c33">I</font> = <font color="Maroon" title="c30">I1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E10:29_1_1_3_1_1_2"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">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="c27">t</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="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E35:29_1_1"><i><font color="Green" title="E32">LM6S1</font></i></a>, <a class="txt" href="#E36:29_1_1"><i><font color="Green" title="E33">LM6S2</font></i></a>, <a class="txt" href="#E37:29_1_1"><i><font color="Green" title="E34">LM6S3</font></i></a>, <a class="txt" href="#E40:29_1_1"><i><font color="Green" title="E36">LM6S4</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c34">O</font> = <font color="Maroon" title="c31">O1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E12:29_1_1_3_1_1_2"/>
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c32">CS</font>,<font color="Maroon" title="c33">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c32">CS</font>,<font color="Maroon" title="c34">O</font>
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_2"><i><font color="Green" title="E45">S5</font></i></a>, <a class="txt" href="petri_2.html#E22"><i><font color="Green" title="E14">LM7</font></i></a>, <a class="txt" href="#E44:29_1_1"><i><font color="Green" title="E40">LM7T</font></i></a>, <a class="txt" href="#E5:29_1_1_3_1_1_2"><i><font color="Green" title="E46">T6</font></i></a></i>;<br/><b>hence </b><a NAME="E13:29_1_1_3_1_1_2"/>
 ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font>
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:29_1_1_3_1_1_3"/><i><font color="Green" title="E45">S6</font></i>: 
<font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font></span><br/><div class="add"><b>reconsider </b><font color="Maroon" title="c28">t1</font> = <font color="Maroon" title="c27">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_3"><i><font color="Green" title="E45">S6</font></i></a>, <a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a></i>;<br/><a NAME="E3:29_1_1_3_1_1_3"/><i><font color="Green" title="E46">S610</font></i>: 
 ex <font color="Olive" title="b1">x1</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="Maroon" title="c28">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> &amp; <font color="Olive" title="b1">x1</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_3"><i><font color="Green" title="E45">S6</font></i></a>, <a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a></i>;<br/><a NAME="E4:29_1_1_3_1_1_3"/><i><font color="Green" title="E47">T6</font></i>: 
<font color="Maroon" title="c5">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c28">t1</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Maroon" title="c28">t1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="txt" href="#E3:29_1_1_3_1_1_3"><i><font color="Green" title="E46">S610</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">CS</font> = the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c30">I</font> =  <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="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E29:29_1_1"><i><font color="Green" title="E27">LM6T1</font></i></a>, <a class="txt" href="#E30:29_1_1"><i><font color="Green" title="E28">LM6T2</font></i></a>, <a class="txt" href="#E31:29_1_1"><i><font color="Green" title="E29">LM6T3</font></i></a>, <a class="txt" href="#E34:29_1_1"><i><font color="Green" title="E31">LM6T4</font></i></a></i>;<br/><a NAME="E7:29_1_1_3_1_1_3"/>
 <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Maroon" title="c28">t1</font> <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="c27">t</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> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_3_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c31">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="c31">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Maroon" title="c28">t1</font> or <font color="Maroon" title="c31">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="c27">t</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="E1:29_1_1_3_1_1_3_1"/><i><font color="Green" title="E48">Z</font></i>: 
<font color="Maroon" title="c31">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Maroon" title="c28">t1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c31">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="c27">t</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 reconsider </b><font color="Maroon" title="c32">s</font> = <font color="Maroon" title="c31">x</font> as   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c2">CPNT2</font> ;<br/>
<a NAME="E3:29_1_1_3_1_1_3_1"/><i><font color="Green" title="E49">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c28">t1</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">O12</font>
 
<b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_3_1"><i><font color="Green" title="E48">Z</font></i></a>, <a class="ref" href="relset_2.html#T9" title="RELSET_2:th.9">RELSET_2:9</a></i>;<br/>
<a NAME="E4:29_1_1_3_1_1_3_1"/><i><font color="Green" title="E50">A5</font></i>: 
<font color="Maroon" title="c7">O12</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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="E5:29_1_1_3_1_1_3_1"/>
<font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<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="E6:29_1_1_3_1_1_3_1"/><b>then </b>
<font color="Maroon" title="c7">O12</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a>, <a class="txt" href="#E4:29_1_1_3_1_1_3_1"><i><font color="Green" title="E50">A5</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c33">f</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c27">t</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="txt" href="#E3:29_1_1_3_1_1_3_1"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>
<a NAME="E8:29_1_1_3_1_1_3_1"/><i><font color="Green" title="E51">A4</font></i>: 
<font color="Maroon" title="c32">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font>
 
;<br/>
<a NAME="E9:29_1_1_3_1_1_3_1"/><i><font color="Green" title="E52">A31</font></i>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="E10:29_1_1_3_1_1_3_1"/>
( <font color="Maroon" title="c27">t</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="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c33">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="c27">t</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:29_1_1_3_1_1_3_1"/>
<font color="Maroon" title="c31">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="c27">t</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="#E9:29_1_1_3_1_1_3_1"><i><font color="Green" title="E52">A31</font></i></a>, <a class="txt" href="#E8:29_1_1_3_1_1_3_1"><i><font color="Green" title="E51">A4</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>then reconsider </b><font color="Maroon" title="c31">O</font> =  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c7">O12</font>,<font color="Maroon" title="c28">t1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> ;<br/><a NAME="E9:29_1_1_3_1_1_3"/>
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS</font>,<font color="Maroon" title="c30">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS</font>,<font color="Maroon" title="c31">O</font>
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_3"><i><font color="Green" title="E45">S6</font></i></a>, <a class="txt" href="petri_2.html#E22"><i><font color="Green" title="E14">LM7</font></i></a>, <a class="txt" href="#E44:29_1_1"><i><font color="Green" title="E40">LM7T</font></i></a>, <a class="txt" href="#E4:29_1_1_3_1_1_3"><i><font color="Green" title="E47">T6</font></i></a></i>;<br/><b>hence </b><a NAME="E10:29_1_1_3_1_1_3"/>
 ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font>
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_3_1_1_4"><b>suppose </b></a><a NAME="E1:29_1_1_3_1_1_4"/><i><font color="Green" title="E45">S7</font></i>: 
<font color="Maroon" title="c27">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font></span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c28">t1</font> = <font color="Maroon" title="c27">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font> <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a></i>;<br/><a NAME="E3:29_1_1_3_1_1_4"/><i><font color="Green" title="E46">S610</font></i>: 
 ex <font color="Olive" title="b1">x1</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font> st <br/>( <font color="Maroon" title="c28">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x1</font> &amp; <font color="Olive" title="b1">x1</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_4"><i><font color="Green" title="E45">S7</font></i></a>, <a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a></i>;<br/><a NAME="E4:29_1_1_3_1_1_4"/><i><font color="Green" title="E47">T6</font></i>: 
<font color="Maroon" title="c6">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c28">t1</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Maroon" title="c28">t1</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="txt" href="#E3:29_1_1_3_1_1_4"><i><font color="Green" title="E46">S610</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">CS</font> = the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c30">I</font> =  <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="c28">t1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E35:29_1_1"><i><font color="Green" title="E32">LM6S1</font></i></a>, <a class="txt" href="#E36:29_1_1"><i><font color="Green" title="E33">LM6S2</font></i></a>, <a class="txt" href="#E37:29_1_1"><i><font color="Green" title="E34">LM6S3</font></i></a>, <a class="txt" href="#E40:29_1_1"><i><font color="Green" title="E36">LM6S4</font></i></a></i>;<br/><a NAME="E7:29_1_1_3_1_1_4"/>
 <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Maroon" title="c28">t1</font> <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="c27">t</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> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_3_1_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c31">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="c31">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Maroon" title="c28">t1</font> or <font color="Maroon" title="c31">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="c27">t</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="E1:29_1_1_3_1_1_4_1"/><i><font color="Green" title="E48">Z</font></i>: 
<font color="Maroon" title="c31">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Maroon" title="c28">t1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c31">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="c27">t</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 reconsider </b><font color="Maroon" title="c32">s</font> = <font color="Maroon" title="c31">x</font> as   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c1">CPNT1</font> ;<br/>
<a NAME="E3:29_1_1_3_1_1_4_1"/><i><font color="Green" title="E49">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c28">t1</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">O21</font>
 
<b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_4_1"><i><font color="Green" title="E48">Z</font></i></a>, <a class="ref" href="relset_2.html#T9" title="RELSET_2:th.9">RELSET_2:9</a></i>;<br/>
<a NAME="E4:29_1_1_3_1_1_4_1"/><i><font color="Green" title="E50">A5</font></i>: 
<font color="Maroon" title="c8">O21</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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="E5:29_1_1_3_1_1_4_1"/>
<font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c33">f</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c27">t</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>, <a class="txt" href="#E3:29_1_1_3_1_1_4_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="#E4:29_1_1_3_1_1_4_1"><i><font color="Green" title="E50">A5</font></i></a></i>;<br/>
<a NAME="E7:29_1_1_3_1_1_4_1"/><i><font color="Green" title="E51">A4</font></i>: 
<font color="Maroon" title="c32">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font>
 
;<br/>
<a NAME="E8:29_1_1_3_1_1_4_1"/><i><font color="Green" title="E52">A31</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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="E9:29_1_1_3_1_1_4_1"/>
( <font color="Maroon" title="c27">t</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="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c33">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="c27">t</font>,<font color="Maroon" title="c32">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:29_1_1_3_1_1_4_1"/>
<font color="Maroon" title="c31">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="c27">t</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="#E8:29_1_1_3_1_1_4_1"><i><font color="Green" title="E52">A31</font></i></a>, <a class="txt" href="#E7:29_1_1_3_1_1_4_1"><i><font color="Green" title="E51">A4</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>then reconsider </b><font color="Maroon" title="c31">O</font> =  <a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c8">O21</font>,<font color="Maroon" title="c28">t1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> ;<br/><a NAME="E9:29_1_1_3_1_1_4"/>
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS</font>,<font color="Maroon" title="c30">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c29">CS</font>,<font color="Maroon" title="c31">O</font>
 <b>by </b><i><a class="txt" href="#E1:29_1_1_3_1_1_4"><i><font color="Green" title="E45">S7</font></i></a>, <a class="txt" href="petri_2.html#E22"><i><font color="Green" title="E14">LM7</font></i></a>, <a class="txt" href="#E44:29_1_1"><i><font color="Green" title="E40">LM7T</font></i></a>, <a class="txt" href="#E4:29_1_1_3_1_1_4"><i><font color="Green" title="E47">T6</font></i></a></i>;<br/><b>hence </b><a NAME="E10:29_1_1_3_1_1_4"/>
 ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font>
 ; <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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:29_1_1_3"/>
 ex <font color="Olive" title="b1">CS</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) ex <font color="Olive" title="b2">I</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c27">t</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>)</span> st the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c27">t</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b2">I</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Olive" title="b1">CS</font>,<font color="Olive" title="b3">O</font>
 ; <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>
<a NAME="E48:29_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c27">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="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) or <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:29_1_1_4"/><i><font color="Green" title="E44">ASD</font></i>: 
<font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span>)</span></span><br/>

<b>then reconsider </b><font color="Maroon" title="c28">t</font> = <font color="Maroon" title="c27">x</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="txt" href="#E45:29_1_1"><i><font color="Green" title="E41">s10</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c29">RR1</font> = the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font>;<br/>
<b>set </b><font color="Maroon" title="c30">RR2</font> = the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font>;<br/>
<b>set </b><font color="Maroon" title="c31">RR3</font> = <font color="Maroon" title="c5">q12</font>;<br/>
<b>set </b><font color="Maroon" title="c32">RR4</font> = <font color="Maroon" title="c6">q21</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_4_1_1"/>
( <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> or <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font> or <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font> or <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font> )
 </span><b>by </b><i><a class="txt" href="#E1:29_1_1_4"><i><font color="Green" title="E44">ASD</font></i></a>, <a class="txt" href="#E28:29_1_1"><i><font color="Green" title="E26">P22</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:29_1_1_4_1_1_1"/><i><font color="Green" title="E45">CAS1</font></i>: 
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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"> not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span><br/><div class="add"><a NAME="E2:29_1_1_4_1_1_1"/><i><font color="Green" title="E46">Q0</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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="c1">CPNT1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><a NAME="E3:29_1_1_4_1_1_1"/><b>then </b><i><font color="Green" title="E47">Q1</font></i>: 
( <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> &amp; not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font> )
 <b>by </b><i><a class="txt" href="#E1:29_1_1_4_1_1_1"><i><font color="Green" title="E45">CAS1</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c33">t1</font> = <font color="Maroon" title="c28">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> <b>by </b><i><a class="txt" href="#E2:29_1_1_4_1_1_1"><i><font color="Green" title="E46">Q0</font></i></a>, <a class="txt" href="#E1:29_1_1_4_1_1_1"><i><font color="Green" title="E45">CAS1</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E5:29_1_1_4_1_1_1"/>
not <font color="Maroon" title="c33">t1</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>
 <b>by </b><i><a class="txt" href="#E3:29_1_1_4_1_1_1"><i><font color="Green" title="E47">Q1</font></i></a></i>;<br/><a NAME="E6:29_1_1_4_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c33">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="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a></i>;<br/><a NAME="E7:29_1_1_4_1_1_1"/><b>then </b><i><font color="Green" title="E48">Q2</font></i>: 
 ex <font color="Olive" title="b1">g</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">g</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="c33">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> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E8:29_1_1_4_1_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c33">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="c28">t</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="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E29:29_1_1"><i><font color="Green" title="E27">LM6T1</font></i></a>, <a class="txt" href="#E30:29_1_1"><i><font color="Green" title="E28">LM6T2</font></i></a>, <a class="txt" href="#E31:29_1_1"><i><font color="Green" title="E29">LM6T3</font></i></a>, <a class="txt" href="#E34:29_1_1"><i><font color="Green" title="E31">LM6T4</font></i></a></i>;<br/><a NAME="E9:29_1_1_4_1_1_1"/><b>then </b>
for <font color="Olive" title="b1">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)  holds <br/>(  not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font> or  not <font color="Olive" title="b1">w</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a>, <a class="txt" href="#E7:29_1_1_4_1_1_1"><i><font color="Green" title="E48">Q2</font></i></a></i>;<br/><b>hence </b><a NAME="E10:29_1_1_4_1_1_1"/>
not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:29_1_1_4_1_1_2"/><i><font color="Green" title="E45">CAS2</font></i>: 
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</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"> not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span><br/><div class="add"><a NAME="E2:29_1_1_4_1_1_2"/><i><font color="Green" title="E46">Q0</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font></span>)</span>
 <b>by </b><i><a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/><a NAME="E3:29_1_1_4_1_1_2"/><b>then </b><i><font color="Green" title="E47">Q1</font></i>: 
( <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font> )
 <b>by </b><i><a class="txt" href="#E1:29_1_1_4_1_1_2"><i><font color="Green" title="E45">CAS2</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c33">t1</font> = <font color="Maroon" title="c28">t</font> as   <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font> <b>by </b><i><a class="txt" href="#E2:29_1_1_4_1_1_2"><i><font color="Green" title="E46">Q0</font></i></a>, <a class="txt" href="#E1:29_1_1_4_1_1_2"><i><font color="Green" title="E45">CAS2</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E5:29_1_1_4_1_1_2"/>
not <font color="Maroon" title="c33">t1</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>
 <b>by </b><i><a class="txt" href="#E3:29_1_1_4_1_1_2"><i><font color="Green" title="E47">Q1</font></i></a></i>;<br/><a NAME="E6:29_1_1_4_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c33">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="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a></i>;<br/><a NAME="E7:29_1_1_4_1_1_2"/><b>then </b><i><font color="Green" title="E48">Q2</font></i>: 
 ex <font color="Olive" title="b1">g</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">g</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="c33">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> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E8:29_1_1_4_1_1_2"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c33">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="c28">t</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="ref" href="petri_2.html#T7" target="_self" title="PETRI_2:th.7">LM6</a>, <a class="txt" href="#E35:29_1_1"><i><font color="Green" title="E32">LM6S1</font></i></a>, <a class="txt" href="#E36:29_1_1"><i><font color="Green" title="E33">LM6S2</font></i></a>, <a class="txt" href="#E37:29_1_1"><i><font color="Green" title="E34">LM6S3</font></i></a>, <a class="txt" href="#E40:29_1_1"><i><font color="Green" title="E36">LM6S4</font></i></a></i>;<br/><a NAME="E9:29_1_1_4_1_1_2"/><b>then </b>
for <font color="Olive" title="b1">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)  holds <br/>(  not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font> or  not <font color="Olive" title="b1">w</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a>, <a class="txt" href="#E7:29_1_1_4_1_1_2"><i><font color="Green" title="E48">Q2</font></i></a></i>;<br/><b>hence </b><a NAME="E10:29_1_1_4_1_1_2"/>
not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4_1_1_3"><b>suppose </b></a><a NAME="E1:29_1_1_4_1_1_3"/><i><font color="Green" title="E45">CAS3</font></i>: 
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">q12</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span><br/><div class="add"><a NAME="E2:29_1_1_4_1_1_3"/>
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">O12</font>
 <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="txt" href="#E1:29_1_1_4_1_1_3"><i><font color="Green" title="E45">CAS3</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c33">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:29_1_1_4_1_1_3"/><i><font color="Green" title="E46">FF</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c28">t</font>,<font color="Maroon" title="c33">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">O12</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c34">s</font> = <font color="Maroon" title="c33">s</font> as   <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="#E4:29_1_1_4_1_1_3"><i><font color="Green" title="E46">FF</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E6:29_1_1_4_1_1_3"/><i><font color="Green" title="E47">A5</font></i>: 
<font color="Maroon" title="c7">O12</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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="E7:29_1_1_4_1_1_3"/>
<font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <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="E8:29_1_1_4_1_1_3"/><b>then </b>
<font color="Maroon" title="c7">O12</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a>, <a class="txt" href="#E6:29_1_1_4_1_1_3"><i><font color="Green" title="E47">A5</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c35">f</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c28">t</font>,<font color="Maroon" title="c34">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="txt" href="#E4:29_1_1_4_1_1_3"><i><font color="Green" title="E46">FF</font></i></a></i>;<br/><a NAME="E10:29_1_1_4_1_1_3"/><i><font color="Green" title="E48">A4</font></i>: 
<font color="Maroon" title="c34">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font>
 ;<br/><a NAME="E11:29_1_1_4_1_1_3"/><i><font color="Green" title="E49">A31</font></i>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="E12:29_1_1_4_1_1_3"/>
( <font color="Maroon" title="c28">t</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="c28">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c35">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="c28">t</font>,<font color="Maroon" title="c34">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E13:29_1_1_4_1_1_3"/><b>then </b>
<font color="Maroon" title="c34">s</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="c28">t</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="#E10:29_1_1_4_1_1_3"><i><font color="Green" title="E48">A4</font></i></a>, <a class="txt" href="#E11:29_1_1_4_1_1_3"><i><font color="Green" title="E49">A31</font></i></a></i>;<br/><a NAME="E14:29_1_1_4_1_1_3"/><b>then </b>
for <font color="Olive" title="b1">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)  holds <br/>(  not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font> or  not <font color="Olive" title="b1">w</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a></i>;<br/><b>hence </b><a NAME="E15:29_1_1_4_1_1_3"/>
not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_4_1_1_4"><b>suppose </b></a><a NAME="E1:29_1_1_4_1_1_4"/><i><font color="Green" title="E45">CAS4</font></i>: 
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">q21</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span><br/><div class="add"><a NAME="E2:29_1_1_4_1_1_4"/>
<font color="Maroon" title="c28">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">O21</font>
 <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="txt" href="#E1:29_1_1_4_1_1_4"><i><font color="Green" title="E45">CAS4</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c33">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:29_1_1_4_1_1_4"/><i><font color="Green" title="E46">FF</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c28">t</font>,<font color="Maroon" title="c33">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">O21</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D4" title="RELAT_1:def.4">RELAT_1:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c34">s</font> = <font color="Maroon" title="c33">s</font> as   <a href="petri.html#NM2" title="PETRI:NM.2">place</a> of <font color="Maroon" title="c1">CPNT1</font> <b>by </b><i><a class="txt" href="#E4:29_1_1_4_1_1_4"><i><font color="Green" title="E46">FF</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E6:29_1_1_4_1_1_4"/><i><font color="Green" title="E47">A5</font></i>: 
<font color="Maroon" title="c8">O21</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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="E7:29_1_1_4_1_1_4"/>
<font color="Maroon" title="c17">E31</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c18">E32</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <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="E8:29_1_1_4_1_1_4"/><b>then </b>
<font color="Maroon" title="c8">O21</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 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a>, <a class="txt" href="#E6:29_1_1_4_1_1_4"><i><font color="Green" title="E47">A5</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c35">f</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c28">t</font>,<font color="Maroon" title="c34">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="petri.html#NM7" title="PETRI:NM.7">T-S_arc</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <b>by </b><i><a class="txt" href="#E4:29_1_1_4_1_1_4"><i><font color="Green" title="E46">FF</font></i></a></i>;<br/><a NAME="E10:29_1_1_4_1_1_4"/><i><font color="Green" title="E48">A4</font></i>: 
<font color="Maroon" title="c34">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font>
 ;<br/><a NAME="E11:29_1_1_4_1_1_4"/><i><font color="Green" title="E49">A31</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="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</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="E12:29_1_1_4_1_1_4"/>
( <font color="Maroon" title="c28">t</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="c28">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c35">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="c28">t</font>,<font color="Maroon" title="c34">s</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E13:29_1_1_4_1_1_4"/><b>then </b>
<font color="Maroon" title="c34">s</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="c28">t</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="#E11:29_1_1_4_1_1_4"><i><font color="Green" title="E49">A31</font></i></a>, <a class="txt" href="#E10:29_1_1_4_1_1_4"><i><font color="Green" title="E48">A4</font></i></a></i>;<br/><a NAME="E14:29_1_1_4_1_1_4"/><b>then </b>
for <font color="Olive" title="b1">w</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)  holds <br/>(  not <font color="Maroon" title="c28">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font> or  not <font color="Olive" title="b1">w</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> )
 <b>by </b><i><a class="ref" href="petri_2.html#D8" target="_self" title="PETRI_2:def.8">Def7</a></i>;<br/><b>hence </b><a NAME="E15:29_1_1_4_1_1_4"/>
not <font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)
 ; <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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:29_1_1_4"/>
<font color="Maroon" title="c27">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #)</span>)</span>
 <b>by </b><i><a class="txt" href="#E1:29_1_1_4"><i><font color="Green" title="E44">ASD</font></i></a>, <a class="txt" href="#E46:29_1_1"><i><font color="Green" title="E42">S10</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</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>
<a NAME="E49:29_1_1"/><b>then </b>
 <a href="petri_2.html#G1" title="PETRI_2:aggr.1">Colored_PT_net_Str</a>(# <font color="Maroon" title="c9">P12</font>,<font color="Maroon" title="c10">T12</font>,<font color="Maroon" title="c13">ST12</font>,<font color="Maroon" title="c19">TS12</font>,<font color="Maroon" title="c20">CS12</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c5">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">q21</font></span>)</span> #) is <a href="petri_2.html#V3" title="PETRI_2:attr.3">Colored-PT-net-like</a>
 
<b>by </b><i><a class="txt" href="#E47:29_1_1"><i><font color="Green" title="E43">SS1</font></i></a>, <a class="ref" href="petri_2.html#D10" target="_self" title="PETRI_2:def.10">Def4</a></i>;<br/>
<b>hence </b><a NAME="E50:29_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="petri_2.html#V1" title="PETRI_2:attr.1">strict</a> <a href="petri_2.html#NM2" title="PETRI_2:NM.2">Colored-PT-net</a> ex <font color="Olive" title="b2">q12</font>, <font color="Olive" title="b3">q21</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ex <font color="Olive" title="b4">O12</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font> ex <font color="Olive" title="b5">O21</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> st <br/>( <font color="Maroon" title="c3">O</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="b4">O12</font>,<font color="Olive" title="b5">O21</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">q12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c1">CPNT1</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b3">q21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K7" title="PETRI_2:func.7">Outbds</a> <font color="Maroon" title="c2">CPNT2</font> &amp; ( for <font color="Olive" title="b6">t01</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font>  st <font color="Olive" title="b6">t01</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> holds <br/><font color="Olive" title="b2">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b6">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O12</font>,<font color="Olive" title="b6">t01</font></span>)</span> ) &amp; ( for <font color="Olive" title="b6">t02</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c2">CPNT2</font>  st <font color="Olive" title="b6">t02</font> is <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a> holds <br/><font color="Olive" title="b3">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b6">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font>,<span class="p1">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b5">O21</font>,<font color="Olive" title="b6">t02</font></span>)</span> ) &amp; <font color="Maroon" title="c4">q</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="Olive" title="b2">q12</font>,<font color="Olive" title="b3">q21</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O12</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b5">O21</font> &amp; the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c2">CPNT2</font> &amp; the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c1">CPNT1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c2">CPNT2</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b3">q21</font> )
 <b>by </b><i><a class="txt" href="#E2:29_1_1"><i><font color="Green" title="E20">P1</font></i></a>, <a class="txt" href="#E27:29_1_1"><i><font color="Green" title="E25">P2</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>
