- EXISTS_PROCESS
-
|- ?P. (\(A,TR). IS_PROCESS (A,TR)) P
- PROCESS_LEMMA1
-
|- !a a'. (REP_process a = REP_process a') = a = a'
- PROCESS_LEMMA2
-
|- !r. IS_PROCESS r = (?a. r = REP_process a)
- PROCESS_LEMMA3
-
|- !r r'.
IS_PROCESS r ==>
IS_PROCESS r' ==>
((ABS_process r = ABS_process r') = r = r')
- PROCESS_LEMMA4
-
|- !a. ?r. (a = ABS_process r) /\ IS_PROCESS r
- PROCESS_LEMMA5
-
|- !a. ABS_process (REP_process a) = a
- PROCESS_LEMMA6
-
|- !r. IS_PROCESS r = REP_process (ABS_process r) = r
- ID_PROCESS
-
|- !P. ABS_process (ALPHA P,TRACES P) = P
- ID_PROCESS'
-
|- !P. (ALPHA P,TRACES P) = REP_process P
- proc_LEMMA1
-
|- !P v. (P = ABS_process v) /\ IS_PROCESS v ==> [] IN TRACES P
- proc_LEMMA2
-
|- !P v.
(P = ABS_process v) /\ IS_PROCESS v ==>
(!s t. APPEND s t IN TRACES P ==> s IN TRACES P)
- proc_LEMMA3
-
|- !P v.
(P = ABS_process v) /\ IS_PROCESS v ==> TRACES P SUBSET STAR (ALPHA P)
- NIL_IN_TRACES
-
|- !P. [] IN TRACES P
- APPEND_IN_TRACES
-
|- !P s t. APPEND s t IN TRACES P ==> s IN TRACES P
- TRACES_IN_STAR
-
|- !P. TRACES P SUBSET STAR (ALPHA P)
- ALPHA_FST
-
|- !x y. IS_PROCESS (x,y) ==> (ALPHA (ABS_process (x,y)) = x)
- TRACES_SND
-
|- !x y. IS_PROCESS (x,y) ==> (TRACES (ABS_process (x,y)) = y)
- PROCESS_EQ_SPLIT
-
|- !P Q. (P = Q) = (ALPHA P = ALPHA Q) /\ (TRACES P = TRACES Q)