Theory: process_ty

Parents


Type constants


Term constants


Axioms


Definitions

IS_PROCESS
|- !A TR.
     IS_PROCESS (A,TR) =
     TR SUBSET STAR A /\ [] IN TR /\ (!s t. APPEND s t IN TR ==> s IN TR)
process_TY_DEF
|- ?rep. TYPE_DEFINITION (\(A,TR). IS_PROCESS (A,TR)) rep
process_ISO_DEF
|- (!a. ABS_process (REP_process a) = a) /\
   (!r. (\(A,TR). IS_PROCESS (A,TR)) r = REP_process (ABS_process r) = r)
ALPHA_DEF
|- !P. ALPHA P = FST (REP_process P)
TRACES_DEF
|- !P. TRACES P = SND (REP_process P)

Theorems

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)