Z is a transition and Z0 is the empty transition. For the definitions
of the operations union, intersection and composition over T see .
The following relations over PN are central for this paper:...
Let us define:...
We shall assume that if a place takes part simultaneously in two or more PNs then it has one and the same notation.
Let us take arbitrary r
and x.For every T there exists W such that p
receives one and the same characteristic in both T and W.We now fix the transitions Z1 and Z2
and construct a new transition, namely Z3.
The last is true because the token
receives one and the
same characteristic in both E1 and E2, since P=Q.
We shall consider that L3 \ L2 6= ; because otherwise the operation composition over PNs is reduced to union. By the defi nition of the operation union over T and the condition E1(; x) = E2(; x), we have that the token receives one and the same characteristic in both transitions.