Volume 4, 1992

University of Bialystok

Copyright (c) 1992 Association of Mizar Users

### The abstract of the Mizar article:

### Definitions of Petri Net. Part III

**by****Waldemar Korczynski**- Received January 31, 1992
- MML identifier: S_SIEC

- [ Mizar article, MML identifier index ]

environ vocabulary E_SIEC, BOOLE, RELAT_1, S_SIEC; notation TARSKI, XBOOLE_0, ZFMISC_1, STRUCT_0, RELAT_1, E_SIEC; constructors E_SIEC; clusters RELAT_1, ZFMISC_1; begin definition let N be e_net; redefine func e_Places N; synonym s_transitions N; redefine func e_Transitions N; synonym s_places N; redefine func e_shore N; synonym s_carrier N; redefine func e_entrance N; synonym s_enter N; redefine func e_escape N; synonym s_exit N; redefine func e_adjac N; synonym s_prox N; end; reserve N for e_net; canceled 40; theorem :: S_SIEC:41 ((the entrance of N) \ diagonal(the carrier of N))~ c= [:e_Places(N),e_Transitions(N):] & ((the escape of N) \ diagonal(the carrier of N))~ c= [:e_Places(N),e_Transitions(N):]; definition let N be G_Net; canceled 27; func s_pre(N) -> Relation equals :: S_SIEC:def 28 ((the escape of N) \ diagonal(the carrier of N))~; func s_post(N) -> Relation equals :: S_SIEC:def 29 ((the entrance of N) \ diagonal(the carrier of N))~; end; canceled; theorem :: S_SIEC:43 s_post(N) c= [:s_transitions(N),s_places(N):] & s_pre(N) c= [:s_transitions(N),s_places(N):];

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