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<span class="kw">let </span><font color="Maroon" title="c5">CA</font>, <font color="Maroon" title="c6">CB</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">q12</font>, <font color="Olive" title="b2">q21</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ex <font color="Olive" title="b3">O12</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b4">O21</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b3">O12</font>,<font color="Olive" title="b4">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="b1">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="b2">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="b5">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="b5">t01</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b1">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b3">O12</font>,<font color="Olive" title="b5">t01</font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive" title="b5">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="b5">t02</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b2">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O21</font>,<font color="Olive" title="b5">t02</font></span>)</span></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="b1">q12</font>,<font color="Olive" title="b2">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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="b3">O12</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O21</font> &amp; the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="b1">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q21</font> ) &amp;  ex <font color="Olive" title="b1">q12</font>, <font color="Olive" title="b2">q21</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ex <font color="Olive" title="b3">O12</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b4">O21</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b3">O12</font>,<font color="Olive" title="b4">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="b1">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="b2">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="b5">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="b5">t01</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b1">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b3">O12</font>,<font color="Olive" title="b5">t01</font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive" title="b5">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="b5">t02</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b2">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O21</font>,<font color="Olive" title="b5">t02</font></span>)</span></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="b1">q12</font>,<font color="Olive" title="b2">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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="b3">O12</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O21</font> &amp; the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="b1">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q21</font> ) implies <font color="Maroon" title="c5">CA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">CB</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:29_1_2"/>
 ex <font color="Olive" title="b1">q12A</font>, <font color="Olive" title="b2">q21A</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ex <font color="Olive" title="b3">O12A</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b4">O21A</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b3">O12A</font>,<font color="Olive" title="b4">O21A</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="b1">q12A</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="b2">q21A</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="b5">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="b5">t01</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b1">q12A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b3">O12A</font>,<font color="Olive" title="b5">t01</font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive" title="b5">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="b5">t02</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b2">q21A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O21A</font>,<font color="Olive" title="b5">t02</font></span>)</span></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="b1">q12A</font>,<font color="Olive" title="b2">q21A</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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="b3">O12A</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O21A</font> &amp; the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c5">CA</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="Maroon" title="c5">CA</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="b1">q12A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q21A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( for <font color="Olive" title="b1">q12</font>, <font color="Olive" title="b2">q21</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/> for <font color="Olive" title="b3">O12</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font><br/> for <font color="Olive" title="b4">O21</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font>  holds <br/>(  not <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="b3">O12</font>,<font color="Olive" title="b4">O21</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or  not  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">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> or  not  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b2">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> or  ex <font color="Olive" title="b5">t01</font> being  <a href="petri.html#NM4" title="PETRI:NM.4">transition</a> of <font color="Maroon" title="c1">CPNT1</font> st <br/>( <font color="Olive" title="b5">t01</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  &amp; <font color="Olive" title="b1">q12</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t01</font> is  not   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b3">O12</font>,<font color="Olive" title="b5">t01</font></span>)</span></span>)</span> ) or  ex <font color="Olive" title="b5">t02</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="Olive" title="b5">t02</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  &amp; <font color="Olive" title="b2">q21</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t02</font> is  not   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O21</font>,<font color="Olive" title="b5">t02</font></span>)</span></span>)</span> ) or  not <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="b1">q12</font>,<font color="Olive" title="b2">q21</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  not the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c6">CB</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> or  not the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c6">CB</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> or  not the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c6">CB</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> or  not the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c6">CB</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="b3">O12</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O21</font> or  not the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c6">CB</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> or  not the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c6">CB</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="b1">q12</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q21</font> ) or <font color="Maroon" title="c5">CA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">CB</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">q12A</font>, <font color="Maroon" title="c8">q21A</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>, <font color="Maroon" title="c9">O12A</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font>, <font color="Maroon" title="c10">O21A</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font><span class="kw"> such that </span><br/><a NAME="E3:29_1_2"/><span class="lab"><font color="Green" title="E20">A74</font></span>: 
<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="c9">O12A</font>,<font color="Maroon" title="c10">O21A</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:29_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">q12A</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>
 <span class="kw">and </span><br/><a NAME="E5:29_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">q21A</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>
 <span class="kw">and </span><br/><a NAME="E6:29_1_2"/>
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="c7">q12A</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 <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><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></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c9">O12A</font>,<font color="Olive" title="b1">t01</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:29_1_2"/>
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="c8">q21A</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 <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><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></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c10">O21A</font>,<font color="Olive" title="b1">t02</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:29_1_2"/><span class="lab"><font color="Green" title="E21">A75</font></span>: 
<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="c7">q12A</font>,<font color="Maroon" title="c8">q21A</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E9:29_1_2"/><span class="lab"><font color="Green" title="E22">A76</font></span>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c5">CA</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>
 <span class="kw">and </span><br/><a NAME="E10:29_1_2"/><span class="lab"><font color="Green" title="E23">A77</font></span>: 
the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c5">CA</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>
 <span class="kw">and </span><br/><a NAME="E11:29_1_2"/><span class="lab"><font color="Green" title="E24">A78</font></span>: 
the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c5">CA</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>
 <span class="kw">and </span><br/><a NAME="E12:29_1_2"/><span class="lab"><font color="Green" title="E25">A79</font></span>: 
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c5">CA</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="c9">O12A</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c10">O21A</font>
 <span class="kw">and </span><br/><a NAME="E13:29_1_2"/><span class="lab"><font color="Green" title="E26">A80</font></span>: 
the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c5">CA</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>
 <span class="kw">and </span><br/><a NAME="E14:29_1_2"/><span class="lab"><font color="Green" title="E27">A81</font></span>: 
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c5">CA</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="Maroon" title="c7">q12A</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">q21A</font>
 ;<br/>
<span class="kw">assume </span><a NAME="E15:29_1_2"/>
 ex <font color="Olive" title="b1">q12B</font>, <font color="Olive" title="b2">q21B</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ex <font color="Olive" title="b3">O12B</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b4">O21B</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,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="b3">O12B</font>,<font color="Olive" title="b4">O21B</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="b1">q12B</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="b2">q21B</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="b5">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="b5">t01</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b1">q12B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t01</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t01</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b3">O12B</font>,<font color="Olive" title="b5">t01</font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive" title="b5">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="b5">t02</font> is  <a href="petri_2.html#V2" title="PETRI_2:attr.2">outbound</a>  holds <br/><font color="Olive" title="b2">q21B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">t02</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b5">t02</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Olive" title="b4">O21B</font>,<font color="Olive" title="b5">t02</font></span>)</span></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="b1">q12B</font>,<font color="Olive" title="b2">q21B</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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="b3">O12B</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b4">O21B</font> &amp; the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c6">CB</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="Maroon" title="c6">CB</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="b1">q12B</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Olive" title="b2">q21B</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">CA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">CB</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">q12B</font>, <font color="Maroon" title="c12">q21B</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>, <font color="Maroon" title="c13">O12B</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c2">CPNT2</font>, <font color="Maroon" title="c14">O21B</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <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>,the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c1">CPNT1</font><span class="kw"> such that </span><br/><a NAME="E17:29_1_2"/><span class="lab"><font color="Green" title="E28">A82</font></span>: 
<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="c13">O12B</font>,<font color="Maroon" title="c14">O21B</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E18:29_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c11">q12B</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>
 <span class="kw">and </span><br/><a NAME="E19:29_1_2"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">q21B</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>
 <span class="kw">and </span><br/><a NAME="E20:29_1_2"/>
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="c11">q12B</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 <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><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></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c13">O12B</font>,<font color="Olive" title="b1">t01</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E21:29_1_2"/>
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="c12">q21B</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 <span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="petri.html#K7" title="PETRI:func.7">*'</a> <span class="p3"><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></span>)</span>,<span class="p1">(<span class="default"><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="p2">(<span class="default"><a href="relset_2.html#K1" title="RELSET_2:func.1">Im</a> <font color="Maroon" title="c14">O21B</font>,<font color="Olive" title="b1">t02</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E22:29_1_2"/><span class="lab"><font color="Green" title="E29">A83</font></span>: 
<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="c11">q12B</font>,<font color="Maroon" title="c12">q21B</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E23:29_1_2"/><span class="lab"><font color="Green" title="E30">A84</font></span>: 
the <a href="petri.html#U1" title="PETRI:sel.1">Places</a> of <font color="Maroon" title="c6">CB</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>
 <span class="kw">and </span><br/><a NAME="E24:29_1_2"/><span class="lab"><font color="Green" title="E31">A85</font></span>: 
the <a href="petri.html#U2" title="PETRI:sel.2">Transitions</a> of <font color="Maroon" title="c6">CB</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>
 <span class="kw">and </span><br/><a NAME="E25:29_1_2"/><span class="lab"><font color="Green" title="E32">A86</font></span>: 
the <a href="petri.html#U3" title="PETRI:sel.3">S-T_Arcs</a> of <font color="Maroon" title="c6">CB</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>
 <span class="kw">and </span><br/><a NAME="E26:29_1_2"/><span class="lab"><font color="Green" title="E33">A87</font></span>: 
the <a href="petri.html#U4" title="PETRI:sel.4">T-S_Arcs</a> of <font color="Maroon" title="c6">CB</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="c13">O12B</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c14">O21B</font>
 <span class="kw">and </span><br/><a NAME="E27:29_1_2"/><span class="lab"><font color="Green" title="E34">A88</font></span>: 
the <a href="petri_2.html#U1" title="PETRI_2:sel.1">ColoredSet</a> of <font color="Maroon" title="c6">CB</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>
 <span class="kw">and </span><br/><a NAME="E28:29_1_2"/><span class="lab"><font color="Green" title="E35">A89</font></span>: 
the <a href="petri_2.html#U2" title="PETRI_2:sel.2">firing-rule</a> of <font color="Maroon" title="c6">CB</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="Maroon" title="c11">q12B</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c12">q21B</font>
 ;<br/>
<a NAME="E29:29_1_2"/><span class="lab"><font color="Green" title="E36">A90</font></span>: 
<font color="Maroon" title="c8">q21A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">q21B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:29_1_2"><span class="lab"><font color="Green" title="E21">A75</font></span></a>, <a class="txt" href="#E22:29_1_2"><span class="lab"><font color="Green" title="E29">A83</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E30:29_1_2"/><span class="lab"><font color="Green" title="E37">A91</font></span>: 
<font color="Maroon" title="c9">O12A</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c13">O12B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1_2"><span class="lab"><font color="Green" title="E20">A74</font></span></a>, <a class="txt" href="#E17:29_1_2"><span class="lab"><font color="Green" title="E28">A82</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E31:29_1_2"/>
<font color="Maroon" title="c7">q12A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">q12B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:29_1_2"><span class="lab"><font color="Green" title="E21">A75</font></span></a>, <a class="txt" href="#E22:29_1_2"><span class="lab"><font color="Green" title="E29">A83</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E32:29_1_2"/>
<font color="Maroon" title="c5">CA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">CB</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:29_1_2"><span class="lab"><font color="Green" title="E20">A74</font></span></a>, <a class="txt" href="#E9:29_1_2"><span class="lab"><font color="Green" title="E22">A76</font></span></a>, <a class="txt" href="#E10:29_1_2"><span class="lab"><font color="Green" title="E23">A77</font></span></a>, <a class="txt" href="#E11:29_1_2"><span class="lab"><font color="Green" title="E24">A78</font></span></a>, <a class="txt" href="#E12:29_1_2"><span class="lab"><font color="Green" title="E25">A79</font></span></a>, <a class="txt" href="#E13:29_1_2"><span class="lab"><font color="Green" title="E26">A80</font></span></a>, <a class="txt" href="#E14:29_1_2"><span class="lab"><font color="Green" title="E27">A81</font></span></a>, <a class="txt" href="#E17:29_1_2"><span class="lab"><font color="Green" title="E28">A82</font></span></a>, <a class="txt" href="#E23:29_1_2"><span class="lab"><font color="Green" title="E30">A84</font></span></a>, <a class="txt" href="#E24:29_1_2"><span class="lab"><font color="Green" title="E31">A85</font></span></a>, <a class="txt" href="#E25:29_1_2"><span class="lab"><font color="Green" title="E32">A86</font></span></a>, <a class="txt" href="#E26:29_1_2"><span class="lab"><font color="Green" title="E33">A87</font></span></a>, <a class="txt" href="#E27:29_1_2"><span class="lab"><font color="Green" title="E34">A88</font></span></a>, <a class="txt" href="#E28:29_1_2"><span class="lab"><font color="Green" title="E35">A89</font></span></a>, <a class="txt" href="#E29:29_1_2"><span class="lab"><font color="Green" title="E36">A90</font></span></a>, <a class="txt" href="#E30:29_1_2"><span class="lab"><font color="Green" title="E37">A91</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
