(MEMBERP)
(UPDATE-MACRO
 (197 91 (:REWRITE DEFAULT-+-2))
 (127 91 (:REWRITE DEFAULT-+-1))
 (72 18 (:REWRITE COMMUTATIVITY-OF-+))
 (72 18 (:DEFINITION INTEGER-ABS))
 (72 9 (:DEFINITION LENGTH))
 (45 9 (:DEFINITION LEN))
 (31 23 (:REWRITE DEFAULT-<-2))
 (27 23 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-UNARY-MINUS))
 (15 15 (:REWRITE DEFAULT-CAR))
 (9 9 (:TYPE-PRESCRIPTION LEN))
 (9 9 (:REWRITE DEFAULT-REALPART))
 (9 9 (:REWRITE DEFAULT-NUMERATOR))
 (9 9 (:REWRITE DEFAULT-IMAGPART))
 (9 9 (:REWRITE DEFAULT-DENOMINATOR))
 (9 9 (:REWRITE DEFAULT-COERCE-2))
 (9 9 (:REWRITE DEFAULT-COERCE-1))
 (3 3 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (1 1 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 )
(SET-HIL-HSL)
(ALL-FALSE)
(KEYS)
(GERMAN-STEP)
(INITIAL-CLIENTS)
(INITIAL-CLIENTS-IDLE
 (14 14 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-CDR))
 )
(INIT)
(COHERENT-PROCESSES)
(COHERENT-PROCESSES-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(COHERENT)
(|initial state is coherent|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE COHERENT-PROCESSES-NECC))
 )
(|coherent default cases|
 (27 9 (:DEFINITION MEMBERP))
 (15 15 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (8 2 (:DEFINITION SET-HIL-HSL))
 (6 2 (:DEFINITION ALL-FALSE))
 )
(COHERENT-AFTER-SETTING-IDLE
 (225 225 (:REWRITE DEFAULT-CDR))
 )
(|coherent after rule 6|
 (6 2 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(CH2-CLIENT-SHARED)
(CH2-CLIENT-SHARED-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(CH2-CLIENT-SHARED-INVARIANT)
(|init has ch2-shared|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE CH2-CLIENT-SHARED-NECC))
 )
(CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE)
(COHERENT-AFTER-SETTING-SHARED
 (25 25 (:REWRITE DEFAULT-CDR))
 )
(|coherent after rule 7|
 (6 2 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(CH2-CLIENT-EXCLUSIVE)
(CH2-CLIENT-EXCLUSIVE-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(CH2-CLIENT-EXCLUSIVE-INVARIANT)
(|init has ch2-exclusive|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE CH2-CLIENT-EXCLUSIVE-NECC))
 )
(CH2-EXCLUSIVE-MEANS-IDLE)
(CH2-EXCLUSIVE-MEANS-SET-IDLE
 (24 8 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(|ch2-exclusive causes coherence|
 (40 40 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|coherent after rule 8|
 (31 31 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 2 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2 shared default cases|
 (186 186 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (10 10 (:REWRITE DEFAULT-CAR))
 (10 2 (:DEFINITION SET-HIL-HSL))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(CH2-SHARED-IF-IDLE
 (75 75 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (74 74 (:REWRITE DEFAULT-CDR))
 (43 43 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2-shared if sharer-invalidate|
 (58 58 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(CH2-CLIENT-SHARED-AFTER-ARBITRARY
 (33 33 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2-client-shared after setting shared|
 (35 35 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (31 31 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2 shared invariant after no grants-shared set|
 (197 197 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (13 13 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE DEFAULT-CAR))
 (12 3 (:DEFINITION ALL-FALSE))
 )
(NOT-HEG-CLIENTS-SHARED)
(NOT-HEG-CLIENTS-SHARED-NECC)
(NOT-HEG-CLIENTS-SHARED-INVARIANT)
(|init has not-heg-shared|
 (9 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE NOT-HEG-CLIENTS-SHARED-NECC))
 )
(NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED
 (12 12 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 9 (:REWRITE DEFAULT-CAR))
 )
(|ch2 shared invariant after home grants shared|
 (77 77 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(CHANNEL-NIL-EXCLUSIVE)
(CHANNEL-NIL-EXCLUSIVE-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(CHANNEL-NIL-EXCLUSIVE-INVARIANT)
(|init has channel-nil-exclusive|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE CHANNEL-NIL-EXCLUSIVE-NECC))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(CHANNEL-NIL-IMPLIES-CH2-CLIENT-SHARED
 (76 2 (:REWRITE CH2-CLIENT-SHARED-AFTER-ARBITRARY))
 (44 44 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (25 25 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED))
 )
(|ch2-shared after client-receives-exclusive|
 (51 49 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (49 49 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2 exclusive default cases|
 (194 190 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (190 190 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (12 2 (:DEFINITION SET-HIL-HSL))
 (10 10 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(CH2-EXCLUSIVE-IF-IDLE
 (65 65 (:REWRITE DEFAULT-CDR))
 (62 22 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (44 44 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 )
(|ch2-exclusive if sharer-invalidate|
 (58 58 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (58 58 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(CH2-CLIENT-EXCLUSIVE-AFTER-ARBITRARY
 (29 29 (:REWRITE DEFAULT-CDR))
 (25 25 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED))
 )
(|ch2 exclusive for invalidate and shared|
 (151 151 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (151 151 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE DEFAULT-CAR))
 )
(NO-GRANT-EXCLUSIVE)
(NO-GRANT-EXCLUSIVE-NECC)
(NO-GRANT-EXCLUSIVE-IMPLIES-CH2-EXCLUSIVE
 (8 8 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT
 (7 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(NO-GRANT-AFTER-SETTING-CHANNEL
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(|ch2 exclusive for client sharing|
 (90 87 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (87 87 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 5 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(CH2-EXCLUSIVE-AFTER-CH2-NIL
 (9 3 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 2 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (4 4 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(CH2-EXCLUSIVE-AFTER-CH2-NIL-2
 (72 2 (:REWRITE CH2-CLIENT-EXCLUSIVE-AFTER-ARBITRARY))
 (42 10 (:DEFINITION MEMBERP))
 (18 18 (:REWRITE DEFAULT-CAR))
 (18 4 (:REWRITE NO-GRANT-EXCLUSIVE-IMPLIES-CH2-EXCLUSIVE))
 (16 16 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (16 14 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (14 14 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 2 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (6 2 (:REWRITE NO-GRANT-AFTER-SETTING-CHANNEL))
 (2 2 (:REWRITE G-DIFF-S))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch2 exclusive for client exclusive|
 (51 49 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (49 49 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (20 20 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (18 6 (:REWRITE NO-GRANT-EXCLUSIVE-IMPLIES-CH2-EXCLUSIVE))
 (12 4 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (9 3 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-CLIENT)
(HSL-CLIENT-INVARIANT)
(HSL-CLIENT-SET
 (31 31 (:REWRITE DEFAULT-CAR))
 (30 30 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (30 30 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(HSL-CLIENT-INITIAL-CLIENT
 (17 3 (:REWRITE INITIAL-CLIENTS-IDLE))
 (16 16 (:REWRITE DEFAULT-CAR))
 (10 3 (:DEFINITION MEMBERP))
 (7 7 (:TYPE-PRESCRIPTION MEMBERP))
 (7 7 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE G-DIFF-S))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|init has hsl-client|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH2-AND-ALL-FALSE
 (27 27 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (23 23 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(HSL-CLIENT-IMPLIES-CH2-EXCLUSIVE
 (11 1 (:DEFINITION HSL-CLIENT))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 2 (:DEFINITION MEMBERP))
 (6 1 (:DEFINITION ALL-FALSE))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:REWRITE NO-GRANT-EXCLUSIVE-IMPLIES-CH2-EXCLUSIVE))
 (2 2 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (1 1 (:REWRITE G-DIFF-S))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-CLIENT-EXCLUSIVE-AFTER-ARBITRARY))
 )
(|ch2-exclusive for home-grants-exclusive|
 (93 88 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (88 88 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (88 88 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (72 6 (:DEFINITION HSL-CLIENT))
 (30 10 (:REWRITE NO-GRANT-EXCLUSIVE-IMPLIES-CH2-EXCLUSIVE))
 (20 20 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (19 19 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE DEFAULT-CDR))
 (18 3 (:DEFINITION ALL-FALSE))
 (11 4 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|not heg shared default cases|
 (265 265 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (265 265 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (265 265 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (26 26 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (14 2 (:DEFINITION SET-HIL-HSL))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-ACK-CLIENTS)
(INVALIDATE-ACK-CLIENTS-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(INVALIDATE-ACK-CLIENTS-INVARIANT)
(|init has invariant-ack-ch3|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE INVALIDATE-ACK-CLIENTS-NECC))
 )
(INVALIDATE-ACK-IMPLIES-NOT-HEG
 (3 1 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(|heg-shared after home-receives-invalidate|
 (63 63 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (63 63 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (63 63 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(NOT-HEG-CLIENTS-SHARED-REMAINS-WITH-SHARED
 (6 6 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (6 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(|heg-shared after client-receives-shared|
 (107 107 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (107 107 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (107 107 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (13 13 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 )
(HEG-EXCLUSIVE)
(HEG-EXCLUSIVE-NECC)
(HEG-EXCLUSIVE-INVARIANT)
(|init has heg-exclusive|
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION MEMBERP))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE HEG-EXCLUSIVE-NECC))
 )
(HEG-EXCLUSIVE-AND-GRANT-IMPLIES-NOT-HEG
 (4 1 (:REWRITE NOT-HEG-CLIENTS-SHARED-REMAINS-WITH-SHARED))
 (3 1 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE G-DIFF-S))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(|heg shared after client-receives-exclusive|
 (53 53 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (53 53 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (53 53 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(HEG-IMPLIES-ANYTHING-FINE
 (1 1 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 )
(|heg shared after home-grants-exclusive|
 (75 75 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (75 75 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (75 75 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (18 3 (:DEFINITION ALL-FALSE))
 (10 10 (:REWRITE INVALIDATE-ACK-IMPLIES-NOT-HEG))
 (9 3 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|channel-nil-exclusive default cases|
 (88 88 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (88 88 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (88 88 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (30 10 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (20 20 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (14 2 (:DEFINITION SET-HIL-HSL))
 (9 9 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(CHANNEL-SET-TO-NIL-IMPLIES-CHANNEL-NIL
 (108 22 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (94 54 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (89 17 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (75 75 (:REWRITE DEFAULT-CDR))
 (72 72 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (54 54 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (54 54 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (42 14 (:REWRITE NO-GRANT-AFTER-SETTING-CHANNEL))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|channels-nil when ch2 set to nil|
 (93 81 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (81 81 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (81 81 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (21 7 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (14 14 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH2)
(HSL-CH2-INVARIANT)
(HSL-CH2-NIL
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hsl-ch2|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL
 (41 41 (:REWRITE DEFAULT-CAR))
 (38 38 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (38 38 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (38 38 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (12 12 (:REWRITE DEFAULT-CDR))
 )
(HSL-CH2-IMPLIES-CHANNEL-NIL-EXCLUSIVE
 (78 6 (:DEFINITION HSL-CH2))
 (42 6 (:DEFINITION ALL-FALSE))
 (37 37 (:REWRITE DEFAULT-CDR))
 (24 24 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (24 24 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 2 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (4 4 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 )
(|channel-nil-exclusive grant-exclusive|
 (54 38 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (41 36 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (36 36 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (36 36 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (30 2 (:DEFINITION HSL-CH2))
 (18 4 (:DEFINITION MEMBERP))
 (14 2 (:DEFINITION ALL-FALSE))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE DEFAULT-CAR))
 (9 3 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (6 6 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 )
(HEG-EXCLUSIVE-AND-NOT-HEG-IMPLIES-NO-EXCLUSIVE
 (24 24 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (15 15 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (12 4 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 )
(|channel-nil-exclusive grant-shared|
 (37 31 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (31 31 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (31 31 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (31 31 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (6 6 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (6 2 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(HIL-HEG)
(HIL-HEG-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(HIL-HEG-INVARIANT)
(|init has hil-heg|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE HIL-HEG-NECC))
 )
(HIL-HEG-SET-REDUCTION
 (13 13 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (13 13 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (13 13 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (13 13 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-HEG-CHANNELS-NIL
 (18 18 (:REWRITE DEFAULT-CDR))
 (6 2 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (2 2 (:REWRITE HEG-EXCLUSIVE-AND-NOT-HEG-IMPLIES-NO-EXCLUSIVE))
 )
(|channels-nil for invalidate|
 (116 101 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (101 101 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (101 101 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (101 101 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (21 7 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (15 5 (:DEFINITION MEMBERP))
 (14 14 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 )
(|hsl-client default cases|
 (572 319 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (319 319 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (319 319 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (319 319 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (230 23 (:DEFINITION ALL-FALSE))
 (115 115 (:TYPE-PRESCRIPTION ALL-FALSE))
 (104 104 (:REWRITE DEFAULT-CAR))
 (102 102 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE HIL-HEG-SET-REDUCTION))
 (20 20 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (16 2 (:DEFINITION SET-HIL-HSL))
 )
(HSL-SET-REDUCTION
 (257 48 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (200 17 (:DEFINITION ALL-FALSE))
 (79 79 (:TYPE-PRESCRIPTION ALL-FALSE))
 (49 49 (:REWRITE DEFAULT-CAR))
 (48 48 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (48 48 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (48 48 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (27 27 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE HIL-HEG-SET-REDUCTION))
 (13 13 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hsl-clients if hsl set to T|
 (250 173 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (173 173 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (173 173 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (173 173 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (91 10 (:DEFINITION ALL-FALSE))
 (54 54 (:REWRITE DEFAULT-CDR))
 (54 54 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE HIL-HEG-SET-REDUCTION))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-IDLE-REDUCTION
 (13 1 (:DEFINITION HSL-CLIENT))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|hsl-clients if clients idle|
 (113 80 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (80 80 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (80 80 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (80 80 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (30 3 (:DEFINITION ALL-FALSE))
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (15 15 (:TYPE-PRESCRIPTION ALL-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-IDLE-REDUCTION-2
 (354 59 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (279 24 (:DEFINITION ALL-FALSE))
 (114 114 (:TYPE-PRESCRIPTION ALL-FALSE))
 (59 59 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (59 59 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (59 59 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (53 53 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(INVALIDATE-ACK-IDLE)
(INVALIDATE-ACK-IDLE-NECC)
(INVALIDATE-ACK-IDLE-INVARIANT)
(|init has invalidate-ack-idle|
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION MEMBERP))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE INVALIDATE-ACK-IDLE-NECC))
 )
(INVALIDATE-ACK-HSL
 (16 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (13 1 (:DEFINITION HSL-CLIENT))
 (10 1 (:DEFINITION ALL-FALSE))
 (5 5 (:TYPE-PRESCRIPTION ALL-FALSE))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|hsl-clients if hsl set|
 (116 83 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (83 83 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (83 83 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (83 83 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (30 3 (:DEFINITION ALL-FALSE))
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (15 15 (:TYPE-PRESCRIPTION ALL-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CH2-SET-REDUCTION
 (38 16 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (20 2 (:DEFINITION ALL-FALSE))
 (18 18 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (16 16 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (10 10 (:TYPE-PRESCRIPTION ALL-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(HSL-CH2-SET
 (351 147 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (187 17 (:DEFINITION ALL-FALSE))
 (156 156 (:REWRITE DEFAULT-CAR))
 (147 147 (:REWRITE HSL-CH2-SET-REDUCTION))
 (147 147 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (147 147 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (147 147 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (85 85 (:TYPE-PRESCRIPTION ALL-FALSE))
 (67 67 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE HIL-HEG-SET-REDUCTION))
 (29 29 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-HSL-CLIENT-PACKAGED
 (25 6 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (22 1 (:DEFINITION HSL-CLIENT))
 (18 1 (:DEFINITION ALL-FALSE))
 (15 1 (:DEFINITION HSL-CH2))
 (8 8 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (7 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 5 (:TYPE-PRESCRIPTION ALL-FALSE))
 )
(|hsl-client for client-receives|
 (275 167 (:REWRITE HSL-CH2-SET-REDUCTION))
 (241 149 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (239 167 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (167 167 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (167 167 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (144 8 (:DEFINITION ALL-FALSE))
 (105 7 (:DEFINITION HSL-CH2))
 (70 70 (:REWRITE DEFAULT-CAR))
 (52 52 (:REWRITE DEFAULT-CDR))
 (40 40 (:TYPE-PRESCRIPTION ALL-FALSE))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|ch3-client default cases|
 (309 309 (:REWRITE HSL-CH2-SET-REDUCTION))
 (309 309 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (309 309 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (309 309 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (309 309 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (34 34 (:REWRITE HIL-HEG-SET-REDUCTION))
 (34 34 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (24 3 (:DEFINITION ALL-FALSE))
 (18 2 (:DEFINITION SET-HIL-HSL))
 (16 16 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-ACK-DOES-NOT-CHANGE-IF-SET
 (50 50 (:REWRITE HSL-CH2-SET-REDUCTION))
 (50 50 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (50 50 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (50 50 (:REWRITE DEFAULT-CDR))
 (50 50 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (50 50 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (13 13 (:REWRITE HIL-HEG-SET-REDUCTION))
 (13 13 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|invalidate-ack for home-receives-invalidate|
 (52 52 (:REWRITE HSL-CH2-SET-REDUCTION))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (52 52 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (52 52 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-CLIENTS)
(INVALIDATE-CLIENTS-INVARIANT)
(INVALIDATE-CLIENTS-FOR-NIL
 (6 6 (:REWRITE HSL-CH2-SET-REDUCTION))
 (6 6 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (6 6 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 )
(|init has invalidate-clients|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(INVALIDATE-CLIENTS-IMPLIES-SHARED-OR-EXCLUSIVE
 (27 27 (:REWRITE HSL-CH2-SET-REDUCTION))
 (27 27 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (27 27 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (27 27 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (27 27 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (26 26 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(INVALIDATE-AND-EXCLUSIVE-IMPLIES-INVALIDATE-EXCLUSIVE
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE HSL-CH2-SET-REDUCTION))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1 1 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(INVALIDATE-CLIENTS-AND-COHERENT-IMPLIES-INVALIDATE-ACK
 (119 11 (:REWRITE INVALIDATE-ACK-DOES-NOT-CHANGE-IF-SET))
 (43 43 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE DEFAULT-CAR))
 (30 30 (:REWRITE HSL-CH2-SET-REDUCTION))
 (30 30 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (30 30 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (30 30 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (30 30 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (5 5 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(INVALIDATE-CLIENTS-AND-COHERENT-FOR-EXCLUSIVE
 (23 1 (:DEFINITION INVALIDATE-CLIENTS))
 (6 2 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HSL-CH2-SET-REDUCTION))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(VALID-STATUS)
(VALID-STATUS-INVARIANT)
(SETTING-VALID-DOES-NOT-CHANGE-STATUS
 (154 154 (:REWRITE DEFAULT-CAR))
 (153 153 (:REWRITE HSL-CH2-SET-REDUCTION))
 (153 153 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (153 153 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (153 153 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (153 153 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (90 90 (:REWRITE HIL-HEG-SET-REDUCTION))
 (90 90 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (75 75 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(VALID-STATUS-IN-INITIAL
 (35 5 (:REWRITE INITIAL-CLIENTS-IDLE))
 (22 5 (:DEFINITION MEMBERP))
 (19 19 (:REWRITE DEFAULT-CAR))
 (17 17 (:TYPE-PRESCRIPTION MEMBERP))
 (8 8 (:REWRITE HSL-CH2-SET-REDUCTION))
 (8 8 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (8 8 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE G-DIFF-S))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|init has valid status|)
(NO-EXCLUSIVE)
(NO-EXCLUSIVE-IMPLIES-ALL-IDLE-SHARED
 (34 34 (:REWRITE DEFAULT-CAR))
 (32 32 (:REWRITE HSL-CH2-SET-REDUCTION))
 (32 32 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (32 32 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (32 32 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (32 32 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 15 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(EXCLUSIVE-WITNESS)
(EXCLUSIVE-IMPLIES-EXCLUSIVE-WITNESS
 (80 80 (:REWRITE DEFAULT-CAR))
 (59 59 (:REWRITE HSL-CH2-SET-REDUCTION))
 (59 59 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (59 59 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (59 59 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (59 59 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (40 40 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (27 27 (:REWRITE DEFAULT-CDR))
 )
(NO-EXCLUSIVE-IMPLIES-INVALIDATE-ACK-CLIENTS
 (184 4 (:REWRITE INVALIDATE-ACK-DOES-NOT-CHANGE-IF-SET))
 (138 6 (:DEFINITION VALID-STATUS))
 (72 72 (:REWRITE HSL-CH2-SET-REDUCTION))
 (72 72 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (72 72 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (72 72 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (72 72 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (66 66 (:REWRITE DEFAULT-CDR))
 (60 60 (:REWRITE DEFAULT-CAR))
 (54 6 (:DEFINITION NO-EXCLUSIVE))
 (30 30 (:REWRITE HIL-HEG-SET-REDUCTION))
 (30 30 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (12 12 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (12 4 (:REWRITE INVALIDATE-CLIENTS-AND-COHERENT-IMPLIES-INVALIDATE-ACK))
 (8 8 (:TYPE-PRESCRIPTION COHERENT-PROCESSES))
 (4 4 (:REWRITE INVALIDATE-CLIENTS-AND-COHERENT-FOR-EXCLUSIVE))
 )
(INVALIDATE-COHERENT-VALID-STATUS-INVALIDATE-ACK
 (46 2 (:DEFINITION VALID-STATUS))
 (46 2 (:DEFINITION INVALIDATE-CLIENTS))
 (18 2 (:DEFINITION NO-EXCLUSIVE))
 (16 16 (:REWRITE HSL-CH2-SET-REDUCTION))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (16 16 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (6 2 (:DEFINITION MEMBERP))
 )
(|invalidate-ack-clients for sharer-invalidate-cache|
 (115 5 (:DEFINITION VALID-STATUS))
 (115 5 (:DEFINITION INVALIDATE-CLIENTS))
 (109 109 (:REWRITE HSL-CH2-SET-REDUCTION))
 (109 109 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (109 109 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (109 109 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (109 109 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (33 33 (:REWRITE DEFAULT-CDR))
 (33 33 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(CH2-SHARED-IMPLIES-INVALIDATE-ACK-CLIENTS
 (38 38 (:REWRITE DEFAULT-CDR))
 (31 31 (:REWRITE DEFAULT-CAR))
 (24 24 (:REWRITE HSL-CH2-SET-REDUCTION))
 (24 24 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (24 24 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (24 24 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (5 5 (:REWRITE NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED))
 )
(|invalidate-ack-clients for grant-shared|
 (53 53 (:REWRITE HSL-CH2-SET-REDUCTION))
 (53 53 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (53 53 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (53 53 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (53 53 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE NOT-HEG-CLIENTS-SHARED-IMPLIES-CH2-SHARED))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(INVALIDATE-EXCLUSIVE)
(INVALIDATE-EXCLUSIVE-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(INVALIDATE-EXCLUSIVE-INVARIANT)
(|init has invalidate-exclusive|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE INVALIDATE-EXCLUSIVE-NECC))
 )
(INVALIDATE-EXCLUSIVE-IMPLIES-GRANT-EXCLUSIVE
 (11 11 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE HSL-CH2-SET-REDUCTION))
 (10 10 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (10 10 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (10 10 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|invalidate-ack-clients after client-receives-exclusive|
 (53 53 (:REWRITE HSL-CH2-SET-REDUCTION))
 (53 53 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (53 53 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (53 53 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (53 53 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(|valid-status default cases|
 (210 210 (:REWRITE HSL-CH2-SET-REDUCTION))
 (210 210 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (210 210 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (210 210 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (210 210 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (69 69 (:REWRITE DEFAULT-CAR))
 (67 67 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE HIL-HEG-SET-REDUCTION))
 (20 20 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (18 18 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (18 2 (:DEFINITION SET-HIL-HSL))
 (16 2 (:DEFINITION ALL-FALSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|valid-status non-default cases|
 (161 7 (:DEFINITION VALID-STATUS))
 (111 111 (:REWRITE HSL-CH2-SET-REDUCTION))
 (111 111 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (111 111 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (111 111 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (111 111 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (27 27 (:REWRITE DEFAULT-CDR))
 (27 27 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|heg-exclusive defaults cases|
 (154 154 (:REWRITE HSL-CH2-SET-REDUCTION))
 (154 154 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (154 154 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (154 154 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (154 154 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (18 2 (:DEFINITION SET-HIL-HSL))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 )
(HEG-EXCLUSIVE-IF-HEG-T
 (3 1 (:DEFINITION MEMBERP))
 (1 1 (:REWRITE HSL-CH2-SET-REDUCTION))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|heg exclusive home-grants-exclusive|
 (71 71 (:REWRITE HSL-CH2-SET-REDUCTION))
 (71 71 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (71 71 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (71 71 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (61 61 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (24 3 (:DEFINITION ALL-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HEG-EXCLUSIVE-IF-CHANNEL-SET
 (12 4 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HSL-CH2-SET-REDUCTION))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|heg-exclusive for ch2 set|
 (397 397 (:REWRITE HSL-CH2-SET-REDUCTION))
 (397 397 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (397 397 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (397 397 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (355 355 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (24 24 (:REWRITE HIL-HEG-SET-REDUCTION))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (24 3 (:DEFINITION ALL-FALSE))
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-EXCLUSIVE-IMPLIES-NOT-HEG-IS-FINE
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE HEG-EXCLUSIVE-IF-HEG-T))
 )
(|heg-exclusive for home-receives-invalidate|
 (70 70 (:REWRITE HSL-CH2-SET-REDUCTION))
 (70 70 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (70 70 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (70 70 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (63 63 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (35 7 (:REWRITE HEG-EXCLUSIVE-IF-HEG-T))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-ch2 default cases|
 (442 200 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (213 213 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (213 213 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (213 213 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (198 11 (:DEFINITION ALL-FALSE))
 (101 101 (:REWRITE DEFAULT-CAR))
 (64 64 (:REWRITE DEFAULT-CDR))
 (55 55 (:TYPE-PRESCRIPTION ALL-FALSE))
 (32 2 (:DEFINITION SET-HIL-HSL))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-CH2-AFTER-SETTING-HSL
 (94 32 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (45 45 (:REWRITE DEFAULT-CAR))
 (33 33 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (33 33 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (33 33 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (18 18 (:REWRITE HIL-HEG-SET-REDUCTION))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (18 1 (:DEFINITION ALL-FALSE))
 (17 17 (:REWRITE DEFAULT-CDR))
 (5 5 (:TYPE-PRESCRIPTION ALL-FALSE))
 )
(|hsl-ch2 after home sets|
 (363 158 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (171 10 (:DEFINITION ALL-FALSE))
 (168 168 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (168 168 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (168 168 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (86 86 (:REWRITE DEFAULT-CAR))
 (60 60 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CH2-AFTER-CH2-NIL
 (82 28 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (46 46 (:REWRITE DEFAULT-CAR))
 (33 33 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (33 33 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (33 33 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (18 18 (:REWRITE DEFAULT-CDR))
 (18 1 (:DEFINITION ALL-FALSE))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (5 5 (:TYPE-PRESCRIPTION ALL-FALSE))
 )
(|hsl-ch2 after client sets|
 (481 189 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (234 13 (:DEFINITION ALL-FALSE))
 (202 202 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (202 202 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (202 202 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (88 88 (:REWRITE DEFAULT-CAR))
 (65 65 (:TYPE-PRESCRIPTION ALL-FALSE))
 (61 61 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-HSL)
(HIL-HSL-INVARIANT)
(HIL-HSL-FOR-NIL
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hil-hsl|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HIL-HSL-AND-HIL-IMPLIES-HSL
 (17 17 (:REWRITE HSL-CH2-SET-REDUCTION))
 (17 17 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (17 17 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (17 17 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (16 16 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(HSL-HIL-CH2
 (397 224 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (314 314 (:REWRITE DEFAULT-CAR))
 (308 308 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (308 308 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (308 308 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (126 126 (:REWRITE DEFAULT-CDR))
 (39 39 (:REWRITE HIL-HEG-SET-REDUCTION))
 (39 39 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (25 1 (:DEFINITION ALL-FALSE))
 (5 5 (:TYPE-PRESCRIPTION ALL-FALSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-ch2 after home-sends-invalidate|
 (383 152 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (273 193 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (200 8 (:DEFINITION HIL-HSL))
 (200 8 (:DEFINITION ALL-FALSE))
 (188 188 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (188 188 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (188 188 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (81 81 (:REWRITE DEFAULT-CAR))
 (55 55 (:REWRITE DEFAULT-CDR))
 (40 40 (:TYPE-PRESCRIPTION ALL-FALSE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(INVALIDATE-ACK-CH2)
(INVALIDATE-ACK-CH2-INVARIANT)
(INVALIDATE-ACK-CH2-NIL
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has invalidate-ack-ch2|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(INVALIDATE-ACK-CH2-IMPLIES-CAN-SET-HSL
 (3074 429 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2157 96 (:DEFINITION ALL-FALSE))
 (688 688 (:REWRITE DEFAULT-CAR))
 (512 512 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (508 508 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (508 508 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (508 508 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (402 402 (:TYPE-PRESCRIPTION ALL-FALSE))
 (389 389 (:REWRITE DEFAULT-CDR))
 (49 49 (:REWRITE HIL-HEG-SET-REDUCTION))
 (49 49 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hsl-ch2 after home receives invalidate|
 (287 95 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (210 5 (:DEFINITION INVALIDATE-ACK-CH2))
 (160 8 (:DEFINITION ALL-FALSE))
 (106 106 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (103 103 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (103 103 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (103 103 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (56 56 (:REWRITE DEFAULT-CAR))
 (40 40 (:TYPE-PRESCRIPTION ALL-FALSE))
 (37 37 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-heg default cases|
 (132 132 (:REWRITE HSL-CH2-SET-REDUCTION))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (132 132 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (132 132 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (132 132 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(HEG-NIL-TO-HIL-HEG
 (6 2 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE HSL-CH2-SET-REDUCTION))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1 1 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (1 1 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|hil-heg for receive invalidate|
 (152 152 (:REWRITE HSL-CH2-SET-REDUCTION))
 (152 152 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (152 152 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (152 152 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (152 152 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (152 152 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-HEG-CH2-NIL
 (32 32 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE HSL-CH2-SET-REDUCTION))
 (18 18 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (18 18 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (18 18 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (17 17 (:REWRITE HEG-NIL-TO-HIL-HEG))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (14 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-heg for clients|
 (193 193 (:REWRITE HSL-CH2-SET-REDUCTION))
 (193 193 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (193 193 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (193 193 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (193 193 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (193 193 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (126 18 (:REWRITE HEG-NIL-TO-HIL-HEG))
 (17 17 (:REWRITE HIL-HEG-SET-REDUCTION))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 )
(UNIQUE-HIL)
(UNIQUE-HIL-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(UNIQUE-HIL-INVARIANT)
(|init has unique-hil|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE UNIQUE-HIL-NECC))
 )
(UNIQUE-HIL-IMPLIES-CAN-SET-HIL
 (147 147 (:REWRITE DEFAULT-CDR))
 (90 90 (:REWRITE HSL-CH2-SET-REDUCTION))
 (90 90 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (88 88 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (88 88 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (88 88 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (88 88 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (33 33 (:REWRITE HEG-NIL-TO-HIL-HEG))
 (21 21 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-heg when home sends invalidate|
 (199 199 (:REWRITE HSL-CH2-SET-REDUCTION))
 (199 199 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (199 199 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (199 199 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (199 199 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (199 199 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (21 7 (:DEFINITION MEMBERP))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE DEFAULT-CAR))
 )
(HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL
 (60 32 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (32 32 (:REWRITE HSL-CH2-SET-REDUCTION))
 (32 32 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (32 32 (:REWRITE DEFAULT-CAR))
 (32 32 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (32 32 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (27 27 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (13 13 (:REWRITE DEFAULT-CDR))
 )
(HIL-HSL-IMPLIES-HIL-HEG
 (19 1 (:DEFINITION HIL-HSL))
 (15 1 (:DEFINITION ALL-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (8 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE HEG-NIL-TO-HIL-HEG))
 )
(|hil-heg home grants exclusive|
 (171 10 (:DEFINITION ALL-FALSE))
 (166 126 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (126 126 (:REWRITE HSL-CH2-SET-REDUCTION))
 (126 126 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (126 126 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (126 126 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (116 116 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (116 116 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (114 6 (:DEFINITION HIL-HSL))
 (72 9 (:REWRITE HEG-NIL-TO-HIL-HEG))
 (25 25 (:REWRITE DEFAULT-CDR))
 (25 25 (:REWRITE DEFAULT-CAR))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-HEG)
(HSL-HEG-NECC
 (4 4 (:DEFINITION MV-NTH))
 )
(HSL-HEG-INVARIANT)
(|init has hsl-heg-invariant|
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE HSL-HEG-NECC))
 )
(HSL-CH2-SET-HSL-REDUCTION
 (21 21 (:REWRITE DEFAULT-CAR))
 (20 20 (:REWRITE HSL-CH2-SET-REDUCTION))
 (20 20 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (20 20 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (20 20 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (20 20 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (20 20 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (20 20 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-HEG-AND-SET-HSL-TO-HIL-HEG
 (1330 70 (:DEFINITION SET-HIL-HSL))
 (266 14 (:DEFINITION HSL-CH2))
 (192 192 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (191 191 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (191 191 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (191 191 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (174 114 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (144 144 (:REWRITE DEFAULT-CDR))
 (115 115 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (42 2 (:DEFINITION ALL-FALSE))
 (31 31 (:REWRITE HIL-HSL-IMPLIES-HIL-HEG))
 (31 31 (:REWRITE HEG-NIL-TO-HIL-HEG))
 (10 10 (:TYPE-PRESCRIPTION ALL-FALSE))
 )
(|hil-heg after home-picks-request|
 (238 210 (:REWRITE HSL-CH2-SET-REDUCTION))
 (210 210 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (210 210 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (210 210 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (210 210 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (206 206 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (206 206 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (190 10 (:DEFINITION HSL-CH2))
 (76 4 (:DEFINITION SET-HIL-HSL))
 (38 38 (:REWRITE DEFAULT-CAR))
 (30 30 (:REWRITE DEFAULT-CDR))
 (26 10 (:DEFINITION MEMBERP))
 (24 24 (:REWRITE HIL-HEG-SET-REDUCTION))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (14 14 (:REWRITE HIL-HSL-IMPLIES-HIL-HEG))
 )
(|invalidate-ack-idle default cases|
 (309 309 (:REWRITE HSL-CH2-SET-REDUCTION))
 (309 309 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (309 309 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (309 309 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (309 309 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (309 309 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (309 309 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (34 34 (:REWRITE HIL-HEG-SET-REDUCTION))
 (34 34 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (30 3 (:DEFINITION ALL-FALSE))
 (22 2 (:DEFINITION SET-HIL-HSL))
 (16 16 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-ACK-IDLE-IF-OTHER-THAN-INVALIDATE
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|home-receives invalidate correctly|
 (52 52 (:REWRITE HSL-CH2-SET-REDUCTION))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (52 52 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (52 52 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (52 52 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (52 52 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-ACK-IDLE-SET-IDLE
 (87 4 (:REWRITE INVALIDATE-ACK-IDLE-IF-OTHER-THAN-INVALIDATE))
 (33 8 (:DEFINITION MEMBERP))
 (18 18 (:REWRITE HSL-CH2-SET-REDUCTION))
 (18 18 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (18 18 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (18 18 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (18 18 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (18 18 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (11 11 (:REWRITE HIL-HEG-SET-REDUCTION))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(|invalidate-ack-idle after sharer invalidates|
 (59 59 (:REWRITE HSL-CH2-SET-REDUCTION))
 (59 59 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (59 59 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (59 59 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (59 59 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (59 59 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (59 59 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(INVALIDATE-ACK-CH2-DOES-IT
 (21 21 (:REWRITE HSL-CH2-SET-REDUCTION))
 (21 21 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (21 21 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (21 21 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (21 21 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (21 21 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (21 21 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (19 19 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE DEFAULT-CDR))
 )
(NOT-INVALIDATE-ACK-IMPLIES-SET-ANYTHING
 (15 5 (:DEFINITION MEMBERP))
 (9 9 (:REWRITE HSL-CH2-SET-REDUCTION))
 (9 9 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (9 9 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (9 9 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (9 9 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (9 9 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (1 1 (:REWRITE HIL-HEG-SET-REDUCTION))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(INVALIDATE-ACK-CH2-REDUCTION
 (20 1 (:DEFINITION INVALIDATE-ACK-CH2))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 1 (:DEFINITION MEMBERP))
 )
(|invalidate-ack-idle for clients|
 (140 7 (:DEFINITION INVALIDATE-ACK-CH2))
 (119 119 (:REWRITE HSL-CH2-SET-REDUCTION))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (119 119 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (119 119 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (119 119 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (119 119 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (20 20 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|invalidate-exclusive default cases|
 (154 154 (:REWRITE HSL-CH2-SET-REDUCTION))
 (154 154 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (154 154 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (154 154 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (154 154 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (154 154 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (154 154 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (22 2 (:DEFINITION SET-HIL-HSL))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 )
(INVALIDATE-EXCLUSIVE-FOR-NOT-GRANT-EXCLUSIVE
 (22 22 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE HSL-CH2-SET-REDUCTION))
 (12 12 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (12 12 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (12 12 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (12 12 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (12 12 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|invalidate-exclusive for not ch2 exclusive|
 (237 237 (:REWRITE HSL-CH2-SET-REDUCTION))
 (237 237 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (237 237 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (237 237 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (237 237 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (237 237 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (237 237 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (16 16 (:REWRITE HIL-HEG-SET-REDUCTION))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (13 13 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-EXCLUSIVE-AFTER-NOT-EXCLUSIVE
 (20 20 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE HSL-CH2-SET-REDUCTION))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (15 15 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (15 15 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (15 15 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|invalidate-exclusive after home receives invalidate|
 (52 52 (:REWRITE HSL-CH2-SET-REDUCTION))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (52 52 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (52 52 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (52 52 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (52 52 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(CHANNEL-NIL-EXCLUSIVE-IMPLIES-INVALIDATE-EXCLUSIVE
 (1866 16 (:REWRITE INVALIDATE-EXCLUSIVE-FOR-NOT-GRANT-EXCLUSIVE))
 (1572 16 (:REWRITE INVALIDATE-EXCLUSIVE-AFTER-NOT-EXCLUSIVE))
 (347 347 (:REWRITE HSL-CH2-SET-REDUCTION))
 (347 347 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (347 347 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (347 347 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (347 347 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (339 339 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (177 177 (:REWRITE DEFAULT-CDR))
 (60 20 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (40 40 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (39 39 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (36 36 (:REWRITE HIL-HEG-SET-REDUCTION))
 (36 36 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|invalidate-exclusive for sharer invalidate cache|
 (76 64 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (64 64 (:REWRITE HSL-CH2-SET-REDUCTION))
 (64 64 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (64 64 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (64 64 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (64 64 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (64 64 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 5 (:REWRITE NOT-GRANT-EXCLUSIVE-AND-SOMETHING-IMPLIES-NOT-INVARIANT))
 (10 10 (:TYPE-PRESCRIPTION NO-GRANT-EXCLUSIVE))
 (9 3 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-CH3)
(HSL-CH3-INVARIANT)
(HSL-CH3-FOR-NIL
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hsl-ch3-invariant|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH3-ALL-FALSE-TO-NOT-CH3
 (31 31 (:REWRITE DEFAULT-CAR))
 (27 27 (:REWRITE HSL-CH2-SET-REDUCTION))
 (27 27 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (27 27 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (27 27 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (27 27 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (27 27 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (27 27 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (12 12 (:REWRITE DEFAULT-CDR))
 )
(HSL-CH3-ALL-FALSE-IMPLIES-INVALIDATE-EXCLUSIVE
 (21 1 (:DEFINITION HSL-CH3))
 (11 1 (:DEFINITION ALL-FALSE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|invalidate-exclusive for granting exclusive|
 (131 10 (:DEFINITION ALL-FALSE))
 (126 6 (:DEFINITION HSL-CH3))
 (94 94 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (94 94 (:REWRITE HSL-CH2-SET-REDUCTION))
 (94 94 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (94 94 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (94 94 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (94 94 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (94 94 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (94 94 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (25 25 (:REWRITE DEFAULT-CDR))
 (25 25 (:REWRITE DEFAULT-CAR))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-hsl default cases|
 (575 275 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (285 15 (:DEFINITION ALL-FALSE))
 (275 275 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (275 275 (:REWRITE HSL-CH2-SET-REDUCTION))
 (275 275 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (275 275 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (275 275 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (260 260 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (99 99 (:REWRITE DEFAULT-CAR))
 (84 84 (:REWRITE DEFAULT-CDR))
 (75 75 (:TYPE-PRESCRIPTION ALL-FALSE))
 (18 18 (:REWRITE HIL-HEG-SET-REDUCTION))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-BOOLEAN)
(HSL-BOOLEAN-INVARIANT)
(HSL-BOOLEAN-FOR-NIL
 (3 3 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hsl-boolean|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (1 1 (:REWRITE HSL-CH2-SET-REDUCTION))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1 1 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (1 1 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (1 1 (:REWRITE HIL-HEG-SET-REDUCTION))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(HIL-HSL-MEMBERP
 (2018 480 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (1490 64 (:DEFINITION ALL-FALSE))
 (781 781 (:REWRITE HSL-CH2-SET-REDUCTION))
 (781 781 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (781 781 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (781 781 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (480 480 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (480 480 (:REWRITE DEFAULT-CAR))
 (479 479 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (284 284 (:TYPE-PRESCRIPTION ALL-FALSE))
 (244 244 (:REWRITE DEFAULT-CDR))
 (147 147 (:REWRITE HIL-HEG-SET-REDUCTION))
 (147 147 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (16 16 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-HSL-NOT-MEMBERP
 (308 52 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (254 80 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (246 10 (:DEFINITION ALL-FALSE))
 (80 80 (:REWRITE HSL-CH2-SET-REDUCTION))
 (80 80 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (80 80 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (80 80 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (68 68 (:REWRITE DEFAULT-CAR))
 (61 11 (:REWRITE HIL-HSL-MEMBERP))
 (52 52 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (52 52 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (50 50 (:TYPE-PRESCRIPTION ALL-FALSE))
 (28 28 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE HIL-HEG-SET-REDUCTION))
 (22 22 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-HSL-SET-HIL-HSL
 (141 73 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (132 132 (:REWRITE HSL-CH2-SET-REDUCTION))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (132 132 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (132 132 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (101 101 (:REWRITE DEFAULT-CAR))
 (77 77 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (67 67 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (66 2 (:DEFINITION ALL-FALSE))
 (19 19 (:REWRITE DEFAULT-CDR))
 (10 10 (:TYPE-PRESCRIPTION ALL-FALSE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE G-DIFF-S))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-hsl after picking request|
 (152 92 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (99 99 (:REWRITE HSL-CH2-SET-REDUCTION))
 (99 99 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (99 99 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (99 99 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (92 92 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (89 89 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (80 5 (:DEFINITION HSL-BOOLEAN))
 (57 3 (:DEFINITION ALL-FALSE))
 (34 34 (:REWRITE DEFAULT-CAR))
 (34 2 (:DEFINITION SET-HIL-HSL))
 (29 29 (:REWRITE DEFAULT-CDR))
 (15 15 (:TYPE-PRESCRIPTION ALL-FALSE))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-HSL-AFTER-HIL-NIL
 (165 33 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (127 5 (:DEFINITION ALL-FALSE))
 (102 9 (:REWRITE HIL-HSL-MEMBERP))
 (66 66 (:REWRITE DEFAULT-CAR))
 (48 48 (:REWRITE HSL-CH2-SET-REDUCTION))
 (48 48 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (48 48 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (48 48 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (44 44 (:REWRITE DEFAULT-CDR))
 (33 33 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (32 32 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (25 25 (:TYPE-PRESCRIPTION ALL-FALSE))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-hsl after invalidating|
 (308 128 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (171 9 (:DEFINITION ALL-FALSE))
 (132 132 (:REWRITE HSL-CH2-SET-REDUCTION))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (132 132 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (132 132 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (128 128 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (123 123 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (45 45 (:TYPE-PRESCRIPTION ALL-FALSE))
 (44 44 (:REWRITE DEFAULT-CAR))
 (39 39 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE)
(HIL-INVALIDATE-INVARIANT)
(HIL-INVALIDATE-FOR-NIL
 (3 3 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hil invalidate|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HIL-HSL-AFTER-SETTING-HIL
 (866 103 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (740 35 (:DEFINITION ALL-FALSE))
 (166 166 (:TYPE-PRESCRIPTION ALL-FALSE))
 (141 141 (:REWRITE HSL-CH2-SET-REDUCTION))
 (141 141 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (141 141 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (141 141 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (103 103 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (102 102 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (98 98 (:REWRITE DEFAULT-CAR))
 (57 57 (:REWRITE DEFAULT-CDR))
 (19 19 (:REWRITE HIL-HEG-SET-REDUCTION))
 (19 19 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (13 13 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hil-hsl after home-receives-invalidate|
 (258 98 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (215 5 (:DEFINITION HIL-INVALIDATE))
 (152 8 (:DEFINITION ALL-FALSE))
 (103 103 (:REWRITE HSL-CH2-SET-REDUCTION))
 (103 103 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (103 103 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (103 103 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (98 98 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (95 95 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (40 40 (:TYPE-PRESCRIPTION ALL-FALSE))
 (40 40 (:REWRITE DEFAULT-CAR))
 (37 37 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-HSL-AFTER-SETTING-HSL
 (565 56 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (494 23 (:DEFINITION ALL-FALSE))
 (213 10 (:REWRITE HIL-HSL-AFTER-SETTING-HIL))
 (109 109 (:TYPE-PRESCRIPTION ALL-FALSE))
 (81 81 (:REWRITE HSL-CH2-SET-REDUCTION))
 (81 81 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (81 81 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (81 81 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (60 60 (:REWRITE DEFAULT-CAR))
 (56 56 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (55 55 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (35 35 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE HIL-HEG-SET-REDUCTION))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-hsl after granting|
 (313 173 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (181 10 (:DEFINITION ALL-FALSE))
 (175 175 (:REWRITE HSL-CH2-SET-REDUCTION))
 (175 175 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (175 175 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (175 175 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (173 173 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (165 165 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (62 62 (:REWRITE DEFAULT-CAR))
 (54 54 (:REWRITE DEFAULT-CDR))
 (14 14 (:REWRITE HIL-HEG-SET-REDUCTION))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|invalidate-ack-ch2 default cases|
 (200 200 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (200 200 (:REWRITE HSL-CH2-SET-REDUCTION))
 (200 200 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (200 200 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (200 200 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (200 200 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (200 200 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (200 200 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (66 66 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE DEFAULT-CDR))
 (24 2 (:DEFINITION SET-HIL-HSL))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(INVALIDATE-ACK-CH2-WHEN-CH2-NIL
 (48 10 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (38 38 (:REWRITE HSL-CH2-SET-REDUCTION))
 (38 38 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (38 38 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (38 38 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (38 38 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (32 32 (:REWRITE DEFAULT-CAR))
 (31 31 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (31 31 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (31 31 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(INVALIDATE-ACK-CH2-WHEN-CH2-NIL-AND-CH3-ANYTHING
 (73 20 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (63 63 (:REWRITE HSL-CH2-SET-REDUCTION))
 (63 63 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (63 63 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (63 63 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (63 63 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (57 57 (:REWRITE DEFAULT-CAR))
 (56 56 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (56 56 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (56 56 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (34 34 (:REWRITE HIL-HEG-SET-REDUCTION))
 (34 34 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (33 33 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|invalidate-ack-ch2 after ch2 nil|
 (181 181 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (181 181 (:REWRITE HSL-CH2-SET-REDUCTION))
 (181 181 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (181 181 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (181 181 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (181 181 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (181 181 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (181 181 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (52 52 (:REWRITE DEFAULT-CAR))
 (45 45 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(INVALIDATE-ACK-AFTER-CH3-SET
 (27 27 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE HSL-CH2-SET-REDUCTION))
 (26 26 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (26 26 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (26 26 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (26 26 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (25 25 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (25 25 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (25 25 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (8 8 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|invalidate-ack after receiving invalidate|
 (71 71 (:REWRITE HSL-CH2-SET-REDUCTION))
 (71 71 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (71 71 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (71 71 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (71 71 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (68 68 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (68 68 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (68 68 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (22 22 (:REWRITE DEFAULT-CAR))
 (19 19 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HCM-INVALIDATE-ACK)
(HCM-INVALIDATE-ACK-NECC)
(HCM-INVALIDATE-ACK-INVARIANT)
(|init has hcm-invalidate-ack|
 (4 4 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 1 (:DEFINITION MEMBERP))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE HCM-INVALIDATE-ACK-NECC))
 )
(INVALIDATE-ACK-CH2-WITNESS)
(INVALIDATE-ACK-FROM-WITNESS
 (106 106 (:REWRITE HSL-CH2-SET-REDUCTION))
 (106 106 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (106 106 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (106 106 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (106 106 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (104 104 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (104 104 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (104 104 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (104 104 (:REWRITE DEFAULT-CAR))
 (41 31 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (36 36 (:REWRITE DEFAULT-CDR))
 )
(HCM-INVALIDATE-INVALIDATE-ACK
 (46 2 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (5 5 (:REWRITE HSL-CH2-SET-REDUCTION))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (5 5 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (5 5 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (3 1 (:DEFINITION MEMBERP))
 )
(|invalidate-ack-ch2 when home-grants-shared|
 (4927 31 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (3405 135 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (550 550 (:REWRITE HSL-CH2-SET-REDUCTION))
 (550 550 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (550 550 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (550 550 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (550 550 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (511 511 (:REWRITE DEFAULT-CAR))
 (478 478 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (478 478 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (478 478 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (372 372 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CH3-AND-ALL-FALSE-IMPLIES-OK
 (21 3 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (21 1 (:DEFINITION HSL-CH3))
 (12 12 (:REWRITE DEFAULT-CAR))
 (11 1 (:DEFINITION ALL-FALSE))
 (9 9 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 )
(|invalidate-ack after granting invalidate|
 (5106 138 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (2189 157 (:DEFINITION ALL-FALSE))
 (709 709 (:REWRITE HSL-CH2-SET-REDUCTION))
 (709 709 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (709 709 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (709 709 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (709 709 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (689 689 (:REWRITE DEFAULT-CAR))
 (637 637 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (637 637 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (547 547 (:REWRITE DEFAULT-CDR))
 (126 6 (:DEFINITION HSL-CH3))
 (32 32 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-INVALIDATE-INVALIDATE-ACK-CH2
 (6634 1437 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (4020 4020 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4020 4020 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4020 4020 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4020 4020 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4020 4020 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3845 3845 (:REWRITE DEFAULT-CAR))
 (3197 3197 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3197 3197 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3197 3197 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2923 2923 (:REWRITE DEFAULT-CDR))
 (939 939 (:REWRITE HIL-HEG-SET-REDUCTION))
 (939 939 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (149 149 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (69 69 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-OK))
 (44 44 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|invalidate-ack-ch2 after home-sends-invalidate|
 (7046 44 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (4860 195 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (793 793 (:REWRITE HSL-CH2-SET-REDUCTION))
 (793 793 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (793 793 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (793 793 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (793 793 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (753 753 (:REWRITE DEFAULT-CAR))
 (695 695 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (695 695 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (695 695 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (553 553 (:REWRITE DEFAULT-CDR))
 (216 8 (:DEFINITION HIL-INVALIDATE))
 (44 44 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|unique-hil default cases|
 (237 237 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (237 237 (:REWRITE HSL-CH2-SET-REDUCTION))
 (237 237 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (237 237 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (237 237 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (237 237 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (237 237 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (237 237 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (24 24 (:REWRITE HIL-HEG-SET-REDUCTION))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(UNIQUE-HIL-IMPLIES-SO-AFTER-HIL-NIL
 (61 61 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (35 35 (:REWRITE HSL-CH2-SET-REDUCTION))
 (35 35 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (35 35 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (35 35 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (35 35 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (35 35 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (35 35 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (20 20 (:REWRITE HIL-HEG-SET-REDUCTION))
 (20 20 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (20 20 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|unique-hil after home-sends-invalidate|
 (93 93 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (93 93 (:REWRITE HSL-CH2-SET-REDUCTION))
 (93 93 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (93 93 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (93 93 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (93 93 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (93 93 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (93 93 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (12 4 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(NOT-HEG-IMPLIES-UNIQUE-HIL
 (6 2 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 )
(|unique-hil after home-receives-invalidate|
 (61 61 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (61 61 (:REWRITE HSL-CH2-SET-REDUCTION))
 (61 61 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (61 61 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (61 61 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (61 61 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (61 61 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (61 61 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-HSL-IMPLIES-UNIQUE-HIL
 (105 5 (:DEFINITION HIL-HSL))
 (80 5 (:DEFINITION ALL-FALSE))
 (48 28 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (31 31 (:REWRITE DEFAULT-CDR))
 (28 28 (:REWRITE HSL-CH2-SET-REDUCTION))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (28 28 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (28 28 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (26 26 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (23 23 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE NOT-HEG-IMPLIES-UNIQUE-HIL))
 )
(HIL-HSL-IMPLIES-UNIQUE-HIL-NOT-SET
 (21 1 (:DEFINITION HIL-HSL))
 (16 1 (:DEFINITION ALL-FALSE))
 (8 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 2 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1 1 (:REWRITE NOT-HEG-IMPLIES-UNIQUE-HIL))
 )
(|unique-hil after home grants exclusive|
 (162 9 (:DEFINITION ALL-FALSE))
 (149 113 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (126 6 (:DEFINITION HIL-HSL))
 (113 113 (:REWRITE HSL-CH2-SET-REDUCTION))
 (113 113 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (113 113 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (113 113 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (104 104 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (104 104 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (104 104 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (81 9 (:REWRITE NOT-HEG-IMPLIES-UNIQUE-HIL))
 (24 24 (:REWRITE DEFAULT-CDR))
 (24 24 (:REWRITE DEFAULT-CAR))
 (9 3 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-HEG-IMPLIES-UNIQUE-HIL
 (444 37 (:DEFINITION SET-HIL-HSL))
 (57 57 (:REWRITE DEFAULT-CDR))
 (51 51 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (45 45 (:REWRITE HSL-CH2-SET-REDUCTION))
 (45 45 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (45 45 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (45 45 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (45 45 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (45 45 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (45 45 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (7 7 (:REWRITE NOT-HEG-IMPLIES-UNIQUE-HIL))
 (7 7 (:REWRITE HIL-HSL-IMPLIES-UNIQUE-HIL-NOT-SET))
 )
(|unique-hil after picking new request|
 (81 81 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (81 81 (:REWRITE HSL-CH2-SET-REDUCTION))
 (81 81 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (81 81 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (81 81 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (81 81 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (81 81 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (81 81 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (72 8 (:REWRITE NOT-HEG-IMPLIES-UNIQUE-HIL))
 (24 2 (:DEFINITION SET-HIL-HSL))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HSL-IMPLIES-UNIQUE-HIL-NOT-SET))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE DEFAULT-CDR))
 )
(|hsl-heg default cases|
 (311 311 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (311 311 (:REWRITE HSL-CH2-SET-REDUCTION))
 (311 311 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (311 311 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (311 311 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (311 311 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (311 311 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (311 311 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (34 34 (:REWRITE HIL-HEG-SET-REDUCTION))
 (34 34 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (24 2 (:DEFINITION SET-HIL-HSL))
 (14 14 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 )
(HSL-HEG-AFTER-HEG-NIL
 (6 2 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(|hsl-heg after home receives invalidate|
 (128 128 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (128 128 (:REWRITE HSL-CH2-SET-REDUCTION))
 (128 128 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (128 128 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (128 128 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (128 128 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (128 128 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (128 128 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (11 11 (:REWRITE HIL-HEG-SET-REDUCTION))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(ALL-FALSE-IMPLIES-FALSE
 (12 12 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (9 9 (:REWRITE HSL-CH2-SET-REDUCTION))
 (9 9 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (9 9 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (9 9 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (9 9 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (9 9 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(HSL-CAN-BE-SET-WHEN-ALL-FALSE
 (60 5 (:DEFINITION ALL-FALSE))
 (23 23 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (11 11 (:REWRITE HSL-CH2-SET-REDUCTION))
 (11 11 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (11 11 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (11 11 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (11 11 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (11 11 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 )
(|hsl-heg after home-grants-exclusive|
 (100 10 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 (74 74 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (74 74 (:REWRITE HSL-CH2-SET-REDUCTION))
 (74 74 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (74 74 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (74 74 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (74 74 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (74 74 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (74 74 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (74 74 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (36 3 (:DEFINITION ALL-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-ch3 default cases|
 (715 379 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (379 379 (:REWRITE HSL-CH2-SET-REDUCTION))
 (379 379 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (379 379 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (379 379 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (379 379 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (379 379 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (379 379 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (379 379 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (315 21 (:DEFINITION ALL-FALSE))
 (120 120 (:REWRITE DEFAULT-CAR))
 (118 118 (:REWRITE DEFAULT-CDR))
 (105 105 (:TYPE-PRESCRIPTION ALL-FALSE))
 (28 28 (:REWRITE HIL-HEG-SET-REDUCTION))
 (28 28 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (26 2 (:DEFINITION SET-HIL-HSL))
 )
(HSL-T-DOES-NOT-CHANGE-HSL-CH3
 (352 48 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (295 17 (:DEFINITION ALL-FALSE))
 (79 79 (:TYPE-PRESCRIPTION ALL-FALSE))
 (49 49 (:REWRITE DEFAULT-CAR))
 (48 48 (:REWRITE HSL-CH2-SET-REDUCTION))
 (48 48 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (48 48 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (48 48 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (48 48 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (48 48 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (48 48 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (48 48 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (27 27 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE HIL-HEG-SET-REDUCTION))
 (13 13 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hsl-ch3 does not change on grant|
 (284 172 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (176 173 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (172 172 (:REWRITE HSL-CH2-SET-REDUCTION))
 (172 172 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (172 172 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (172 172 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (172 172 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (172 172 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (172 172 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (141 10 (:DEFINITION ALL-FALSE))
 (55 55 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE DEFAULT-CDR))
 (14 14 (:REWRITE HIL-HEG-SET-REDUCTION))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CH3-IF-CH3-NIL
 (150 39 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (105 6 (:DEFINITION ALL-FALSE))
 (39 39 (:REWRITE HSL-CH2-SET-REDUCTION))
 (39 39 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (39 39 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (39 39 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (39 39 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (39 39 (:REWRITE DEFAULT-CAR))
 (39 39 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (39 39 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (39 39 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (30 30 (:TYPE-PRESCRIPTION ALL-FALSE))
 (22 22 (:REWRITE HIL-HEG-SET-REDUCTION))
 (22 22 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (14 14 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-ch3 after receiving invalidation|
 (169 73 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (90 6 (:DEFINITION ALL-FALSE))
 (73 73 (:REWRITE HSL-CH2-SET-REDUCTION))
 (73 73 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (73 73 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (73 73 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (73 73 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (73 73 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (73 73 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (73 73 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (30 30 (:TYPE-PRESCRIPTION ALL-FALSE))
 (25 25 (:REWRITE DEFAULT-CDR))
 (25 25 (:REWRITE DEFAULT-CAR))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CH3-FOR-NOT-MEMBER
 (216 56 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (150 10 (:DEFINITION ALL-FALSE))
 (60 60 (:REWRITE DEFAULT-CAR))
 (56 56 (:REWRITE HSL-CH2-SET-REDUCTION))
 (56 56 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (56 56 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (56 56 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (56 56 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (56 56 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (56 56 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (56 56 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (50 50 (:TYPE-PRESCRIPTION ALL-FALSE))
 (20 20 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-CH2-IMPLIES-HSL-CH3-AFTER-SET
 (705 177 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (644 28 (:DEFINITION ALL-FALSE))
 (328 176 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (247 247 (:REWRITE DEFAULT-CAR))
 (217 217 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (216 216 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (216 216 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (216 216 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (177 177 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (177 177 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (140 140 (:TYPE-PRESCRIPTION ALL-FALSE))
 (93 93 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE HIL-HEG-SET-REDUCTION))
 (22 22 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-ch3 after sharer invalidates|
 (248 104 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (224 119 (:REWRITE HSL-CH2-SET-REDUCTION))
 (184 8 (:DEFINITION ALL-FALSE))
 (160 104 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (119 119 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (119 119 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (119 119 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (115 5 (:DEFINITION HSL-CH2))
 (104 104 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (104 104 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (53 53 (:REWRITE DEFAULT-CAR))
 (45 19 (:DEFINITION MEMBERP))
 (40 40 (:TYPE-PRESCRIPTION ALL-FALSE))
 (38 38 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hsl-boolean default cases|
 (170 170 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (170 170 (:REWRITE HSL-CH2-SET-REDUCTION))
 (170 170 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (170 170 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (170 170 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (170 170 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (170 170 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (170 170 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (170 170 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (31 31 (:REWRITE DEFAULT-CAR))
 (29 29 (:REWRITE DEFAULT-CDR))
 (26 2 (:DEFINITION SET-HIL-HSL))
 (17 17 (:REWRITE HIL-HEG-SET-REDUCTION))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-BOOLEAN-IF-BOOLEAN-VAL-SET
 (14 14 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (13 13 (:REWRITE HSL-CH2-SET-REDUCTION))
 (13 13 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (13 13 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (13 13 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (13 13 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (13 13 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (13 13 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (13 13 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 )
(|hsl-boolean other cases|
 (104 101 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (100 100 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (100 100 (:REWRITE HSL-CH2-SET-REDUCTION))
 (100 100 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (100 100 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (100 100 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (100 100 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (100 100 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (100 100 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (79 7 (:DEFINITION HSL-BOOLEAN))
 (24 2 (:DEFINITION ALL-FALSE))
 (16 16 (:REWRITE DEFAULT-CAR))
 (15 15 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (2 2 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hil-invalidate default cases|
 (324 324 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (324 324 (:REWRITE HSL-CH2-SET-REDUCTION))
 (324 324 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (324 324 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (324 324 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (324 324 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (324 324 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (324 324 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (324 324 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (93 93 (:REWRITE DEFAULT-CDR))
 (93 93 (:REWRITE DEFAULT-CAR))
 (41 41 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (36 3 (:DEFINITION ALL-FALSE))
 (26 26 (:REWRITE HIL-HEG-SET-REDUCTION))
 (26 26 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-INVALIDATE-ON-NIL
 (32 32 (:REWRITE DEFAULT-CAR))
 (31 31 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (31 31 (:REWRITE HSL-CH2-SET-REDUCTION))
 (31 31 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (31 31 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (31 31 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (31 31 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (31 31 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (31 31 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (31 31 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(|hil-invalidate on home-sends-invalidate|
 (119 119 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (119 119 (:REWRITE HSL-CH2-SET-REDUCTION))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (119 119 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (119 119 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (119 119 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (119 119 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (119 119 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (30 30 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (12 4 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE-ACK-SET
 (29 29 (:REWRITE DEFAULT-CAR))
 (28 28 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (28 28 (:REWRITE HSL-CH2-SET-REDUCTION))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (28 28 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (28 28 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (28 28 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (28 28 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (28 28 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (9 9 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (8 8 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-invalidate when home receives invalidate|
 (68 68 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (68 68 (:REWRITE HSL-CH2-SET-REDUCTION))
 (68 68 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (68 68 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (68 68 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (68 68 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (68 68 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (68 68 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (68 68 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (19 19 (:REWRITE DEFAULT-CDR))
 (19 19 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (9 3 (:DEFINITION MEMBERP))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-INVALIDATE-CH2)
(HIL-INVALIDATE-CH2-INVARIANT)
(HIL-INVALIDATE-CH2-FOR-NIL
 (3 3 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(|init has hil-invalidate-ch2|
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE HIL-HEG-SET-REDUCTION))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HIL-INVALIDATE-CH2-IMPLIES-INVALIDATE
 (232 232 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (232 232 (:REWRITE HSL-CH2-SET-REDUCTION))
 (232 232 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (232 232 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (232 232 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (232 232 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (232 232 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (232 232 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (232 232 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (230 230 (:REWRITE DEFAULT-CAR))
 (70 70 (:REWRITE DEFAULT-CDR))
 (40 40 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (32 32 (:REWRITE HIL-HEG-SET-REDUCTION))
 (32 32 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-invalidate after sharer-invalidate-cache|
 (115 5 (:DEFINITION HIL-INVALIDATE-CH2))
 (96 96 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (96 96 (:REWRITE HSL-CH2-SET-REDUCTION))
 (96 96 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (96 96 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (96 96 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (96 96 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (96 96 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (96 96 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (96 96 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (29 29 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE DEFAULT-CAR))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (5 5 (:REWRITE HIL-HEG-SET-REDUCTION))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE-WITNESS)
(HIL-INVALIDATE-WITNESS-IMPLIES-HIL-INVALIDATE
 (105 105 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (105 105 (:REWRITE HSL-CH2-SET-REDUCTION))
 (105 105 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (105 105 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (105 105 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (105 105 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (105 105 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (105 105 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (105 105 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (99 99 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (34 34 (:REWRITE DEFAULT-CDR))
 )
(HCM-CH3-IMPLIES-HIL-INVALIDATE
 (50 2 (:DEFINITION HIL-INVALIDATE-WITNESS))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (5 5 (:REWRITE HSL-CH2-SET-REDUCTION))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (5 5 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (5 5 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (5 5 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (5 5 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (5 5 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (3 1 (:DEFINITION MEMBERP))
 )
(|hil-invalidate when pick-new-request|
 (3843 21 (:REWRITE HIL-INVALIDATE-WITNESS-IMPLIES-HIL-INVALIDATE))
 (2625 105 (:DEFINITION HIL-INVALIDATE-WITNESS))
 (399 399 (:REWRITE DEFAULT-CAR))
 (390 390 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (390 390 (:REWRITE HSL-CH2-SET-REDUCTION))
 (390 390 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (390 390 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (390 390 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (390 390 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (390 390 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (390 390 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (390 390 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (292 292 (:REWRITE DEFAULT-CDR))
 (261 66 (:DEFINITION MEMBERP))
 (154 154 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (26 2 (:DEFINITION SET-HIL-HSL))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-invalidate-ch2 default cases|
 (191 191 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (191 191 (:REWRITE HSL-CH2-SET-REDUCTION))
 (191 191 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (191 191 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (191 191 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (191 191 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (191 191 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (191 191 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (191 191 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (51 51 (:REWRITE DEFAULT-CDR))
 (51 51 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-INVALIDATE-CH2-WHEN-CH2-NIL
 (29 29 (:REWRITE DEFAULT-CAR))
 (28 28 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (28 28 (:REWRITE HSL-CH2-SET-REDUCTION))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (28 28 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (28 28 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (28 28 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (28 28 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (28 28 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-invalidate-ch2 when ch2 is reset|
 (183 183 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (183 183 (:REWRITE HSL-CH2-SET-REDUCTION))
 (183 183 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (183 183 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (183 183 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (183 183 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (183 183 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (183 183 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (183 183 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (45 45 (:REWRITE DEFAULT-CDR))
 (45 45 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE-CH2-SET-HIL-NIL
 (35 35 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (34 34 (:REWRITE HSL-CH2-SET-REDUCTION))
 (34 34 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (34 34 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (34 34 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (34 34 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (34 34 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (34 34 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (34 34 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (18 18 (:REWRITE HIL-HEG-SET-REDUCTION))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (10 10 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(|hil-invalidate-ch2 home-sends-invalidate|
 (115 115 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (115 115 (:REWRITE HSL-CH2-SET-REDUCTION))
 (115 115 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (115 115 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (115 115 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (115 115 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (115 115 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (115 115 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (115 115 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (30 30 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE DEFAULT-CAR))
 (12 4 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE-OTHER-THAN-INVALIDATE
 (29 29 (:REWRITE DEFAULT-CAR))
 (28 28 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (28 28 (:REWRITE HSL-CH2-SET-REDUCTION))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (28 28 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (28 28 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (28 28 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (28 28 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (28 28 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (28 28 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-invalidate-ch2 for grant|
 (161 161 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (161 161 (:REWRITE HSL-CH2-SET-REDUCTION))
 (161 161 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (161 161 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (161 161 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (161 161 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (161 161 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (161 161 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (161 161 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (47 47 (:REWRITE DEFAULT-CDR))
 (47 47 (:REWRITE DEFAULT-CAR))
 (36 3 (:DEFINITION ALL-FALSE))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HCM-CH2)
(HCM-CH2-NECC)
(HCM-CH2-INVARIANT)
(|init has hcm-ch2|
 (4 4 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 1 (:DEFINITION MEMBERP))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE HCM-CH2-NECC))
 )
(NOT-HCM-IMPLIES-NOT-INVALIDATE)
(HIL-INVALIDATE-RWITNESS)
(HIL-INVALIDATE-RWITNESS-INVALIDATE
 (107 107 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (107 107 (:REWRITE HSL-CH2-SET-REDUCTION))
 (107 107 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (107 107 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (107 107 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (107 107 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (107 107 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (107 107 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (107 107 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (95 95 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE DEFAULT-CDR))
 (34 34 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 )
(NOT-HCM-IMPLIES-HIL-INVALIDATE
 (96 6 (:DEFINITION HIL-INVALIDATE-RWITNESS))
 (20 20 (:REWRITE DEFAULT-CAR))
 (15 15 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (15 15 (:REWRITE HSL-CH2-SET-REDUCTION))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (15 15 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (15 15 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (15 15 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 15 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (12 12 (:REWRITE DEFAULT-CDR))
 )
(|hil-invalidate on pick-new-request|
 (4596 21 (:REWRITE HIL-INVALIDATE-RWITNESS-INVALIDATE))
 (3165 105 (:DEFINITION HIL-INVALIDATE-RWITNESS))
 (838 154 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (487 487 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (487 487 (:REWRITE HSL-CH2-SET-REDUCTION))
 (487 487 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (487 487 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (487 487 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (487 487 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (487 487 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (487 487 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (487 487 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (378 378 (:REWRITE DEFAULT-CAR))
 (271 271 (:REWRITE DEFAULT-CDR))
 (198 45 (:DEFINITION MEMBERP))
 (26 2 (:DEFINITION SET-HIL-HSL))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hcm-ch2 default cases|
 (132 132 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (132 132 (:REWRITE HSL-CH2-SET-REDUCTION))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (132 132 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (132 132 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (132 132 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (132 132 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (132 132 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (132 132 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH3-AND-CH3-TO-HSL
 (48 16 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (30 2 (:DEFINITION ALL-FALSE))
 (18 18 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE HSL-CH2-SET-REDUCTION))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (16 16 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (16 16 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (16 16 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (16 16 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (16 16 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:TYPE-PRESCRIPTION ALL-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 )
(HSL-HEG-HSL-CH3-IMPLIES-ONLY-ONE
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 (1 1 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (1 1 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1 1 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (1 1 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1 1 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1 1 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 )
(HSL-HEG-HSL-CH3-IMPLIES-NONE
 (1385 3 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (955 15 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (944 1 (:DEFINITION INVALIDATE-ACK-CH2))
 (754 31 (:DEFINITION ALL-FALSE))
 (698 75 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (330 67 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (315 92 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (248 112 (:REWRITE HSL-CH2-SET-REDUCTION))
 (235 86 (:DEFINITION MEMBERP))
 (168 168 (:REWRITE DEFAULT-CAR))
 (112 112 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (104 104 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (104 104 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (104 104 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (103 103 (:TYPE-PRESCRIPTION ALL-FALSE))
 (76 76 (:REWRITE DEFAULT-CDR))
 (75 75 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (75 75 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (33 1 (:DEFINITION HSL-CH3))
 (24 1 (:DEFINITION HSL-CH2))
 (3 3 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (1 1 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 )
(HCM-CH2-WHEN-HEG
 (18506 129 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (15799 30 (:DEFINITION INVALIDATE-ACK-CH2))
 (14167 195 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (11800 283 (:DEFINITION ALL-FALSE))
 (11427 787 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3275 981 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (2581 1205 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2486 865 (:DEFINITION MEMBERP))
 (2139 753 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (1730 1730 (:REWRITE DEFAULT-CAR))
 (1354 1 (:DEFINITION HSL-CH2))
 (1205 1205 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (1171 1171 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (1171 1171 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (1171 1171 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (1119 333 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (1099 1099 (:TYPE-PRESCRIPTION ALL-FALSE))
 (787 787 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (787 787 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (784 784 (:REWRITE DEFAULT-CDR))
 (129 129 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (35 1 (:DEFINITION HSL-CH3))
 (1 1 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 )
(|hcm-ch2 when home-receives-invalidate|
 (317583 1610 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (312719 14462 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (286462 263 (:DEFINITION INVALIDATE-ACK-CH2))
 (246796 2720 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (195603 13031 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (192379 4588 (:DEFINITION ALL-FALSE))
 (76939 9 (:REWRITE INVALIDATE-ACK-CH2-WHEN-CH2-NIL))
 (55435 18728 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (50826 23026 (:REWRITE HSL-CH2-SET-REDUCTION))
 (35398 13084 (:DEFINITION MEMBERP))
 (25415 25415 (:REWRITE DEFAULT-CAR))
 (23026 23026 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (22858 22858 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (22858 22858 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (22858 22858 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (22163 5027 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (21730 21730 (:TYPE-PRESCRIPTION ALL-FALSE))
 (19705 12863 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (13031 13031 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (13031 13031 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (12788 12788 (:REWRITE DEFAULT-CDR))
 (7036 12 (:DEFINITION HSL-CH2))
 (7023 69 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-OK))
 (1610 1610 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (332 10 (:DEFINITION HSL-CH3))
 (301 301 (:REWRITE HIL-HEG-SET-REDUCTION))
 (301 301 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (69 69 (:REWRITE HIL-INVALIDATE-INVALIDATE-ACK-CH2))
 (58 58 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING
 (3 3 (:REWRITE HCM-CH2-WHEN-HEG))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (2 2 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 )
(|hcm-ch2 for pick-new-request|
 (75 75 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (75 75 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (75 75 (:REWRITE HSL-CH2-SET-REDUCTION))
 (75 75 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (75 75 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (75 75 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (75 75 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (75 75 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (75 75 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (75 75 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (28 2 (:DEFINITION SET-HIL-HSL))
 (11 11 (:REWRITE HIL-HEG-SET-REDUCTION))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HCM-CH2-WHEN-HEG))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (5 5 (:REWRITE DEFAULT-CDR))
 )
(HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING-WITH-CH2
 (14 14 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (14 14 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (14 14 (:REWRITE HSL-CH2-SET-REDUCTION))
 (14 14 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (14 14 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (14 14 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (14 14 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (14 14 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (14 14 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE HCM-CH2-WHEN-HEG))
 (4 4 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 )
(|hcm-ch2 after home-grants-shared|
 (70 70 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (70 70 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (70 70 (:REWRITE HSL-CH2-SET-REDUCTION))
 (70 70 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (70 70 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (70 70 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (70 70 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (70 70 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (70 70 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (70 70 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:REWRITE HCM-CH2-WHEN-HEG))
 (10 10 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (9 3 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (5 5 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HCM-CH2-IF-THE-RIGHT-THINGS-SET
 (6 2 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (2 2 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE HCM-CH2-WHEN-HEG))
 (2 2 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 )
(|hcm-ch2 when home-sends-invalidate|
 (114 114 (:REWRITE HSL-CH2-SET-REDUCTION))
 (114 114 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (114 114 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (114 114 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (114 114 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (107 107 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (107 107 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (107 107 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (107 107 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (107 107 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (17 17 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (12 4 (:DEFINITION MEMBERP))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE HCM-CH2-WHEN-HEG))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(HCM-CH2-AFTER-SETTING-CH2
 (12 4 (:DEFINITION MEMBERP))
 (10 10 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (10 10 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (10 10 (:REWRITE HSL-CH2-SET-REDUCTION))
 (10 10 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (10 10 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (10 10 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (10 10 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (10 10 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (10 10 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (4 4 (:REWRITE HCM-CH2-WHEN-HEG))
 (4 4 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING-WITH-CH2))
 )
(|hcm-ch2 after client sets|
 (196 196 (:REWRITE HSL-CH2-SET-REDUCTION))
 (196 196 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (196 196 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (196 196 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (196 196 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (178 178 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (178 178 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (178 178 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (178 178 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (178 178 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (126 18 (:REWRITE HCM-CH2-IF-THE-RIGHT-THINGS-SET))
 (36 3 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (24 24 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (18 18 (:REWRITE HCM-CH2-WHEN-HEG))
 (18 18 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (17 17 (:REWRITE HIL-HEG-SET-REDUCTION))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH2-AND-ALL-FALSE-IMPLIES-HCM
 (46 2 (:DEFINITION ALL-FALSE))
 (40 2 (:DEFINITION HSL-CH2))
 (26 10 (:REWRITE HSL-CH2-SET-REDUCTION))
 (20 6 (:DEFINITION MEMBERP))
 (16 10 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (10 10 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (8 8 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (8 8 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (6 6 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (6 6 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE HCM-CH2-WHEN-HEG))
 (2 2 (:REWRITE HCM-CH2-IF-THE-RIGHT-THINGS-SET))
 (2 2 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 )
(|hsm-ch2 when grants exclusive|
 (150 6 (:DEFINITION HSL-CH2))
 (132 108 (:REWRITE HSL-CH2-SET-REDUCTION))
 (120 96 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (108 108 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (108 108 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (108 108 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (108 108 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (100 97 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (97 97 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (96 96 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (96 96 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (69 3 (:DEFINITION ALL-FALSE))
 (35 10 (:DEFINITION MEMBERP))
 (25 25 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (25 25 (:REWRITE DEFAULT-CAR))
 (22 9 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (20 20 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HCM-CH2-WHEN-HEG))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hcm-invalidate-ack default cases|
 (275 275 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (275 275 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (275 275 (:REWRITE HSL-CH2-SET-REDUCTION))
 (275 275 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (275 275 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (275 275 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (275 275 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (275 275 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (275 275 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (275 275 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (30 30 (:REWRITE HIL-HEG-SET-REDUCTION))
 (30 30 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (14 14 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (2 2 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 )
(|hcm-invalidate-ack for pick-new-request|
 (75 75 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (75 75 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (75 75 (:REWRITE HSL-CH2-SET-REDUCTION))
 (75 75 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (75 75 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (75 75 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (75 75 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (75 75 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (75 75 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (75 75 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (28 2 (:DEFINITION SET-HIL-HSL))
 (11 11 (:REWRITE HIL-HEG-SET-REDUCTION))
 (11 11 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (5 5 (:REWRITE DEFAULT-CDR))
 )
(HCM-CH3-AND-NOT-HCM-IMPLIES-HCM-ANYTHING-WITH-CH2
 (14 14 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (14 14 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (14 14 (:REWRITE HSL-CH2-SET-REDUCTION))
 (14 14 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (14 14 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (14 14 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (14 14 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (14 14 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (14 14 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hcm-invalidate-ack after home-grants-shared|
 (73 73 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (73 73 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (73 73 (:REWRITE HSL-CH2-SET-REDUCTION))
 (73 73 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (73 73 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (73 73 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (73 73 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (73 73 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (73 73 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (73 73 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (5 5 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-HEG-HSL-CH3-IMPLIES-ONLY-ONE-CH3
 (2169 106 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2023 6 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (1796 2 (:DEFINITION INVALIDATE-ACK-CH2))
 (1550 25 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (1004 94 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (889 35 (:DEFINITION ALL-FALSE))
 (197 197 (:REWRITE DEFAULT-CAR))
 (131 131 (:REWRITE HSL-CH2-SET-REDUCTION))
 (131 131 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (131 131 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (131 131 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (131 131 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (119 119 (:TYPE-PRESCRIPTION ALL-FALSE))
 (118 118 (:TYPE-PRESCRIPTION INVALIDATE-ACK-CH2))
 (111 111 (:REWRITE DEFAULT-CDR))
 (94 94 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (94 94 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (94 94 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (37 37 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (6 6 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (1 1 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 )
(HCM-CH3-WHEN-HEG
 (63560 3428 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (62400 336 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (50236 72 (:DEFINITION INVALIDATE-ACK-CH2))
 (49786 670 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (41968 2886 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (41732 998 (:DEFINITION ALL-FALSE))
 (10674 2592 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (5408 5408 (:REWRITE DEFAULT-CAR))
 (4766 4766 (:TYPE-PRESCRIPTION ALL-FALSE))
 (4092 4092 (:TYPE-PRESCRIPTION INVALIDATE-ACK-CH2))
 (3470 3470 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3470 3470 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3470 3470 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3470 3470 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3470 3470 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3040 3040 (:REWRITE DEFAULT-CDR))
 (2976 12 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-OK))
 (2886 2886 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2886 2886 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2886 2886 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (1334 1334 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (336 336 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (92 92 (:REWRITE HIL-HEG-SET-REDUCTION))
 (92 92 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (52 2 (:DEFINITION HSL-CH3))
 (12 12 (:REWRITE HIL-INVALIDATE-INVALIDATE-ACK-CH2))
 (2 2 (:REWRITE HSL-HEG-AFTER-HEG-NIL))
 (2 2 (:REWRITE HCM-CH3-AND-NOT-HCM-IMPLIES-HCM-ANYTHING-WITH-CH2))
 (2 2 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 )
(NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK
 (3 1 (:DEFINITION MEMBERP))
 (2 2 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (2 2 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2 2 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2 2 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2 2 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2 2 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2 2 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2 2 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (1 1 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(|hcm-invalidate-ack when home-receives-invalidate|
 (168443 8747 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (163177 796 (:REWRITE INVALIDATE-ACK-FROM-WITNESS))
 (145075 114 (:DEFINITION INVALIDATE-ACK-CH2))
 (126218 1675 (:DEFINITION INVALIDATE-ACK-CH2-WITNESS))
 (101483 7943 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (96244 2742 (:DEFINITION ALL-FALSE))
 (47322 6 (:REWRITE INVALIDATE-ACK-CH2-WHEN-CH2-NIL))
 (29396 7594 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (16102 5459 (:DEFINITION MEMBERP))
 (13672 13672 (:TYPE-PRESCRIPTION ALL-FALSE))
 (12994 12994 (:REWRITE DEFAULT-CAR))
 (10267 10267 (:REWRITE HSL-CH2-SET-REDUCTION))
 (10267 10267 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (10267 10267 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (10267 10267 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (10267 10267 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (10213 10213 (:TYPE-PRESCRIPTION INVALIDATE-ACK-CH2))
 (7943 7943 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (7943 7943 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (7943 7943 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (7797 7797 (:REWRITE DEFAULT-CDR))
 (4582 49 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-OK))
 (3085 3085 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (844 796 (:REWRITE HCM-INVALIDATE-INVALIDATE-ACK))
 (260 10 (:DEFINITION HSL-CH3))
 (224 224 (:REWRITE HIL-HEG-SET-REDUCTION))
 (224 224 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (49 49 (:REWRITE HIL-INVALIDATE-INVALIDATE-ACK-CH2))
 (41 41 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-NOT-A-PROBLEM
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (3 3 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (2 2 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (2 2 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (2 2 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (1 1 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (1 1 (:REWRITE HCM-CH2-WHEN-HEG))
 (1 1 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 )
(|hcm-invalidate-ack after sharer invalidates|
 (98 98 (:REWRITE HSL-CH2-SET-REDUCTION))
 (98 98 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (98 98 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (98 98 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (98 98 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (93 93 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (93 93 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (93 93 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (93 93 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (93 93 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (40 7 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (36 3 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (35 5 (:REWRITE HCM-CH2-IF-THE-RIGHT-THINGS-SET))
 (14 14 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE HIL-HEG-SET-REDUCTION))
 (8 8 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (7 7 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (5 5 (:REWRITE HCM-CH2-WHEN-HEG))
 (5 5 (:REWRITE HCM-CH2-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(HSL-CH3-AND-ALL-FALSE-IMPLIES-HCM
 (46 2 (:DEFINITION ALL-FALSE))
 (40 2 (:DEFINITION HSL-CH3))
 (22 6 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (16 10 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (14 6 (:DEFINITION MEMBERP))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (6 6 (:REWRITE HSL-CH2-SET-REDUCTION))
 (6 6 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (6 6 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2 2 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (2 2 (:REWRITE INVALIDATE-NOT-A-PROBLEM))
 (2 2 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 )
(|hsm-invalidate-ack when grants exclusive|
 (225 9 (:DEFINITION ALL-FALSE))
 (150 6 (:DEFINITION HSL-CH3))
 (119 119 (:REWRITE HSL-CH2-SET-REDUCTION))
 (119 119 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (119 119 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (119 119 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (119 119 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (114 111 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (111 111 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (110 110 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (110 110 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (110 110 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (104 32 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (53 9 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (34 34 (:REWRITE DEFAULT-CAR))
 (29 13 (:DEFINITION MEMBERP))
 (23 23 (:REWRITE DEFAULT-CDR))
 (22 9 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 (9 9 (:REWRITE INVALIDATE-NOT-A-PROBLEM))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|invalidate-clients default cases|
 (273 273 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (273 273 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (273 273 (:REWRITE HSL-CH2-SET-REDUCTION))
 (273 273 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (273 273 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (273 273 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (273 273 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (273 273 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (273 273 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (273 273 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (97 97 (:REWRITE DEFAULT-CAR))
 (95 95 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (29 29 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (28 2 (:DEFINITION SET-HIL-HSL))
 (18 18 (:REWRITE HIL-HEG-SET-REDUCTION))
 (18 18 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (11 11 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-AFTER-SOMETHING-ELSE
 (50 50 (:REWRITE DEFAULT-CAR))
 (49 49 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (49 49 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (49 49 (:REWRITE HSL-CH2-SET-REDUCTION))
 (49 49 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (49 49 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (49 49 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (49 49 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (49 49 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (49 49 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (49 49 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (12 12 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (12 12 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 9 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|invalidate-clients after home-grants|
 (180 180 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (180 180 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (180 180 (:REWRITE HSL-CH2-SET-REDUCTION))
 (180 180 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (180 180 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (180 180 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (180 180 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (180 180 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (180 180 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (180 180 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (66 66 (:REWRITE DEFAULT-CDR))
 (66 66 (:REWRITE DEFAULT-CAR))
 (42 3 (:DEFINITION ALL-FALSE))
 (19 19 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (19 19 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (11 11 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (2 2 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INVALIDATE-AFTER-CLIENT-SET
 (134 134 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (134 134 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (134 134 (:REWRITE HSL-CH2-SET-REDUCTION))
 (134 134 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (134 134 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (134 134 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (134 134 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (134 134 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (134 134 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (134 134 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (133 133 (:REWRITE DEFAULT-CAR))
 (86 86 (:REWRITE DEFAULT-CDR))
 (81 81 (:REWRITE HIL-HEG-SET-REDUCTION))
 (81 81 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (37 37 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (13 13 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|clients are fine with invalidate-clients|
 (198 198 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (198 198 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (198 198 (:REWRITE HSL-CH2-SET-REDUCTION))
 (198 198 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (198 198 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (198 198 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (198 198 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (198 198 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (198 198 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (198 198 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (63 63 (:REWRITE DEFAULT-CDR))
 (63 63 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (18 18 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 )
(HIL-CLIENT-CH2)
(HIL-CLIENT-CH2-INVARIANT)
(HIL-CLIENT-FOR-NIL
 (12 12 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (12 12 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (12 12 (:REWRITE HSL-CH2-SET-REDUCTION))
 (12 12 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (12 12 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (12 12 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (12 12 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (12 12 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (12 12 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (8 8 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (3 3 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|init has hil-client-ch2|
 (3 3 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (3 3 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (3 3 (:REWRITE HSL-CH2-SET-REDUCTION))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (3 3 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (3 3 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (3 3 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (3 3 (:REWRITE HIL-HEG-SET-REDUCTION))
 (3 3 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (3 3 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HIL-CLIENT-CH2-MEMBERP-REDUCTION
 (45 45 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (45 45 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (45 45 (:REWRITE HSL-CH2-SET-REDUCTION))
 (45 45 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (45 45 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (45 45 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (45 45 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (45 45 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (45 45 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (45 45 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (40 40 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(INVALIDATE-CLIENTS-NOT-MEMBERP-REDUCTION
 (190 15 (:REWRITE INVALIDATE-AFTER-SOMETHING-ELSE))
 (92 92 (:REWRITE DEFAULT-CAR))
 (84 84 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (84 84 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (84 84 (:REWRITE HSL-CH2-SET-REDUCTION))
 (84 84 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (84 84 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (84 84 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (84 84 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (84 84 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (84 84 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (84 84 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (20 20 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (14 14 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (11 11 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(HIL-CLIENT-HIL-CH2-REDUCTION
 (755 35 (:REWRITE INVALIDATE-AFTER-SOMETHING-ELSE))
 (473 473 (:REWRITE DEFAULT-CAR))
 (456 456 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (456 456 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (456 456 (:REWRITE HSL-CH2-SET-REDUCTION))
 (456 456 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (456 456 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (456 456 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (456 456 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (456 456 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (456 456 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (456 456 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (128 128 (:REWRITE DEFAULT-CDR))
 (90 90 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (65 65 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (35 35 (:REWRITE HIL-HEG-SET-REDUCTION))
 (35 35 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (33 33 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 )
(|invalidate-clients after home-sends-invalidate|
 (504 8 (:DEFINITION HIL-CLIENT-CH2))
 (194 194 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (194 194 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (194 194 (:REWRITE HSL-CH2-SET-REDUCTION))
 (194 194 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (194 194 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (194 194 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (194 194 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (194 194 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (194 194 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (194 194 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (83 83 (:REWRITE DEFAULT-CDR))
 (83 83 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (18 18 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (13 13 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (12 4 (:DEFINITION MEMBERP))
 (6 6 (:REWRITE HIL-HEG-SET-REDUCTION))
 (6 6 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(|hil-client-ch2 default cases|
 (288 288 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (288 288 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (288 288 (:REWRITE HSL-CH2-SET-REDUCTION))
 (288 288 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (288 288 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (288 288 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (288 288 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (288 288 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (288 288 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (288 288 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (120 120 (:REWRITE DEFAULT-CDR))
 (120 120 (:REWRITE DEFAULT-CAR))
 (29 29 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (23 23 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (15 15 (:REWRITE HIL-HEG-SET-REDUCTION))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (3 3 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-CLIENT-CH2-SET-CH2
 (221 221 (:REWRITE DEFAULT-CAR))
 (220 220 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (220 220 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (220 220 (:REWRITE HSL-CH2-SET-REDUCTION))
 (220 220 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (220 220 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (220 220 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (220 220 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (220 220 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (220 220 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (220 220 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (135 135 (:REWRITE DEFAULT-CDR))
 (41 41 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (40 40 (:REWRITE HIL-HEG-SET-REDUCTION))
 (40 40 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (36 36 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 )
(|hil-client when home grants|
 (246 246 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (246 246 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (246 246 (:REWRITE HSL-CH2-SET-REDUCTION))
 (246 246 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (246 246 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (246 246 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (246 246 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (246 246 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (246 246 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (246 246 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (104 104 (:REWRITE DEFAULT-CDR))
 (104 104 (:REWRITE DEFAULT-CAR))
 (42 3 (:DEFINITION ALL-FALSE))
 (30 30 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (19 19 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (16 16 (:REWRITE HIL-HEG-SET-REDUCTION))
 (16 16 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HIL-CLIENT-CH2-SET-CLIENT
 (3484 188 (:REWRITE HIL-CLIENT-CH2-SET-CH2))
 (454 454 (:REWRITE DEFAULT-CAR))
 (453 453 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (453 453 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (453 453 (:REWRITE HSL-CH2-SET-REDUCTION))
 (453 453 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (453 453 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (453 453 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (453 453 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (453 453 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (453 453 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (453 453 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (323 323 (:REWRITE DEFAULT-CDR))
 (238 238 (:REWRITE HIL-HEG-SET-REDUCTION))
 (238 238 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (84 84 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (72 72 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 )
(|hil-client when client is set|
 (159 159 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (159 159 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (159 159 (:REWRITE HSL-CH2-SET-REDUCTION))
 (159 159 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (159 159 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (159 159 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (159 159 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (159 159 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (159 159 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (159 159 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (61 61 (:REWRITE DEFAULT-CDR))
 (61 61 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (11 11 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-INVALIDATE-IMPLIES-CAN-SET-CLIENT
 (5644 42 (:REWRITE HIL-CLIENT-CH2-SET-CH2))
 (2585 2585 (:REWRITE DEFAULT-CAR))
 (2265 2265 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (2265 2265 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (2265 2265 (:REWRITE HSL-CH2-SET-REDUCTION))
 (2265 2265 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (2265 2265 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (2265 2265 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (2265 2265 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (2265 2265 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (2265 2265 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (2265 2265 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (1842 1842 (:REWRITE DEFAULT-CDR))
 (1054 42 (:REWRITE HIL-CLIENT-CH2-SET-CLIENT))
 (903 903 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (734 734 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (251 251 (:REWRITE HIL-HEG-SET-REDUCTION))
 (251 251 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (119 119 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (59 59 (:REWRITE NOT-HCM-IMPLIES-HIL-INVALIDATE))
 )
(|hil-client for sharer invalidating|
 (3165 15 (:REWRITE HIL-INVALIDATE-RWITNESS-INVALIDATE))
 (2255 5 (:DEFINITION HIL-INVALIDATE-CH2))
 (2100 75 (:DEFINITION HIL-INVALIDATE-RWITNESS))
 (355 355 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (355 355 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (355 355 (:REWRITE HSL-CH2-SET-REDUCTION))
 (355 355 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (355 355 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (355 355 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (355 355 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (355 355 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (355 355 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (355 355 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (308 308 (:REWRITE DEFAULT-CAR))
 (233 233 (:REWRITE DEFAULT-CDR))
 (144 33 (:DEFINITION MEMBERP))
 (136 136 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (113 113 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 (15 15 (:REWRITE NOT-HCM-IMPLIES-HIL-INVALIDATE))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (7 7 (:REWRITE HIL-HEG-SET-REDUCTION))
 (7 7 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HIL-CLIENT-CH2-TO-NIL
 (3116 30 (:REWRITE HIL-CLIENT-CH2-SET-CH2))
 (322 322 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (322 322 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (322 322 (:REWRITE HSL-CH2-SET-REDUCTION))
 (322 322 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (322 322 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (322 322 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (322 322 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (322 322 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (322 322 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (322 322 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (321 321 (:REWRITE DEFAULT-CAR))
 (222 222 (:REWRITE DEFAULT-CDR))
 (69 69 (:REWRITE HIL-HEG-SET-REDUCTION))
 (69 69 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (60 60 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (57 57 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (47 47 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hil-client-ch2 when home-sends-invalidate|
 (173 173 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (173 173 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (173 173 (:REWRITE HSL-CH2-SET-REDUCTION))
 (173 173 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (173 173 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (173 173 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (173 173 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (173 173 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (173 173 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (173 173 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (69 69 (:REWRITE DEFAULT-CDR))
 (69 69 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (13 13 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (12 4 (:DEFINITION MEMBERP))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 )
(HSL-CLIENT-CH2)
(HSL-CLIENT-CH2-INVARIANT)
(HSL-CLIENT-FOR-NIL
 (15 15 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (15 15 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (15 15 (:REWRITE HSL-CH2-SET-REDUCTION))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (15 15 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (15 15 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (15 15 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (15 15 (:REWRITE DEFAULT-CAR))
 (15 15 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (15 15 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (15 15 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (10 10 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (3 3 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(|init has hsl-client-ch2|
 (4 4 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (4 4 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (4 4 (:REWRITE HSL-CH2-SET-REDUCTION))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (4 4 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (4 4 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (4 4 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (4 4 (:REWRITE HIL-HEG-SET-REDUCTION))
 (4 4 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (4 4 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (4 4 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (3 1 (:DEFINITION INITIAL-CLIENTS))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(HIL-CLIENT-WITNESS)
(HIL-CLIENT-WITNESS-TO-HIL-CLIENTS
 (937 937 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (937 937 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (937 937 (:REWRITE HSL-CH2-SET-REDUCTION))
 (937 937 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (937 937 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (937 937 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (937 937 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (937 937 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (937 937 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (937 937 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (886 886 (:REWRITE DEFAULT-CAR))
 (263 263 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (131 131 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (109 109 (:REWRITE DEFAULT-CDR))
 )
(HSL-CLIENT-MEMBER
 (54 54 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (54 54 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (54 54 (:REWRITE HSL-CH2-SET-REDUCTION))
 (54 54 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (54 54 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (54 54 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (54 54 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (54 54 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (54 54 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (54 54 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (47 47 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (8 8 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(HSL-CLIENT-HIL-CLIENT-REDUCTION
 (648 9 (:DEFINITION HIL-CLIENT-WITNESS))
 (168 12 (:DEFINITION SET-HIL-HSL))
 (108 108 (:REWRITE DEFAULT-CAR))
 (91 91 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (91 91 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (91 91 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (79 79 (:REWRITE HSL-CH2-SET-REDUCTION))
 (79 79 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (79 79 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (79 79 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (79 79 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (79 79 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (79 79 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (76 76 (:REWRITE DEFAULT-CDR))
 (76 1 (:DEFINITION HSL-CLIENT-CH2))
 (25 25 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (13 13 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (2 2 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (2 2 (:REWRITE INVALIDATE-NOT-A-PROBLEM))
 (2 2 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (2 2 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-HCM))
 )
(|hil-client-ch2 for picking request|
 (380 5 (:DEFINITION HSL-CLIENT-CH2))
 (181 181 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (181 181 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (181 181 (:REWRITE HSL-CH2-SET-REDUCTION))
 (181 181 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (181 181 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (181 181 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (181 181 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (181 181 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (181 181 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (181 181 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (77 77 (:REWRITE DEFAULT-CAR))
 (75 75 (:REWRITE DEFAULT-CDR))
 (28 2 (:DEFINITION SET-HIL-HSL))
 (18 18 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (13 13 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (12 12 (:REWRITE HIL-HEG-SET-REDUCTION))
 (12 12 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (5 5 (:REWRITE NOT-HEG-INVALIDATE-ACK-IMPLIES-INVALIDATE-ACK))
 (5 5 (:REWRITE INVALIDATE-NOT-A-PROBLEM))
 (5 5 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (5 5 (:REWRITE HSL-CH3-AND-ALL-FALSE-IMPLIES-HCM))
 (5 5 (:REWRITE HCM-ACK-AND-NOT-HCM-IMPLIES-HCM-ANYTHING))
 )
(|hsl-client-ch2 default cases|
 (350 350 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (350 350 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (350 350 (:REWRITE HSL-CH2-SET-REDUCTION))
 (350 350 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (350 350 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (350 350 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (350 350 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (350 350 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (350 350 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (350 350 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (147 147 (:REWRITE DEFAULT-CAR))
 (145 145 (:REWRITE DEFAULT-CDR))
 (32 32 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (28 2 (:DEFINITION SET-HIL-HSL))
 (24 24 (:REWRITE HIL-HEG-SET-REDUCTION))
 (24 24 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (23 23 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (23 23 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(HIL-HSL-AND-HIL-AND-CH2-IMPLIES-HSL
 (468 468 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (468 468 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (468 468 (:REWRITE HSL-CH2-SET-REDUCTION))
 (468 468 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (468 468 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (468 468 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (468 468 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (468 468 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (468 468 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (468 468 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (383 383 (:REWRITE DEFAULT-CAR))
 (133 133 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (65 65 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (50 50 (:REWRITE HIL-HEG-SET-REDUCTION))
 (50 50 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (34 34 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hsl-client-ch2 on home-sends-invalidate|
 (504 8 (:DEFINITION HIL-CLIENT-CH2))
 (271 271 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (271 271 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (271 271 (:REWRITE HSL-CH2-SET-REDUCTION))
 (271 271 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (271 271 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (271 271 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (271 271 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (271 271 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (271 271 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (271 271 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (122 122 (:REWRITE DEFAULT-CDR))
 (122 122 (:REWRITE DEFAULT-CAR))
 (31 31 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (21 21 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (14 14 (:REWRITE HIL-HEG-SET-REDUCTION))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (13 13 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (12 4 (:DEFINITION MEMBERP))
 )
(HSL-CLIENT-RESET-HSL
 (147 147 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (147 147 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (147 147 (:REWRITE HSL-CH2-SET-REDUCTION))
 (147 147 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (147 147 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (147 147 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (147 147 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (147 147 (:REWRITE DEFAULT-CAR))
 (147 147 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (147 147 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (147 147 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (25 25 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (24 24 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (17 17 (:REWRITE HIL-HEG-SET-REDUCTION))
 (17 17 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (11 11 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (10 10 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(|hsl-client-ch2 when home-receives-invalidate|
 (123 123 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (123 123 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (123 123 (:REWRITE HSL-CH2-SET-REDUCTION))
 (123 123 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (123 123 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (123 123 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (123 123 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (123 123 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (123 123 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (123 123 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (51 51 (:REWRITE DEFAULT-CDR))
 (51 51 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (10 10 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (10 10 (:REWRITE HIL-HEG-SET-REDUCTION))
 (10 10 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (3 3 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(HSL-CLIENT-SET-CH3
 (8713 46 (:REWRITE HIL-HSL-AND-HIL-AND-CH2-IMPLIES-HSL))
 (757 757 (:REWRITE DEFAULT-CAR))
 (756 756 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (756 756 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (756 756 (:REWRITE HSL-CH2-SET-REDUCTION))
 (756 756 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (756 756 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (756 756 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (756 756 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (756 756 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (756 756 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (756 756 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (567 567 (:REWRITE DEFAULT-CDR))
 (395 395 (:REWRITE HIL-HEG-SET-REDUCTION))
 (395 395 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (126 126 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (110 110 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (17 17 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hsl-client-ch2 when sharer invalidates|
 (128 128 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (128 128 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (128 128 (:REWRITE HSL-CH2-SET-REDUCTION))
 (128 128 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (128 128 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (128 128 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (128 128 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (128 128 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (128 128 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (128 128 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (51 51 (:REWRITE DEFAULT-CDR))
 (51 51 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (9 9 (:REWRITE HIL-HEG-SET-REDUCTION))
 (9 9 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (9 3 (:DEFINITION MEMBERP))
 (8 8 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (8 8 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (3 3 (:REWRITE NOT-HCM-IMPLIES-NOT-INVALIDATE))
 )
(HSL-CLIENT-CH2-ON-CLIENTS
 (4614 228 (:REWRITE HIL-HSL-AND-HIL-AND-CH2-IMPLIES-HSL))
 (592 592 (:REWRITE DEFAULT-CAR))
 (591 591 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (591 591 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (591 591 (:REWRITE HSL-CH2-SET-REDUCTION))
 (591 591 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (591 591 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (591 591 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (591 591 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (591 591 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (591 591 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (591 591 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (418 418 (:REWRITE DEFAULT-CDR))
 (288 288 (:REWRITE HIL-HEG-SET-REDUCTION))
 (288 288 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (99 99 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (69 69 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (30 30 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hsl-client-ch2 when client sets|
 (187 187 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (187 187 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (187 187 (:REWRITE HSL-CH2-SET-REDUCTION))
 (187 187 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (187 187 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (187 187 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (187 187 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (187 187 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (187 187 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (187 187 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (72 72 (:REWRITE DEFAULT-CDR))
 (72 72 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE HIL-HEG-SET-REDUCTION))
 (14 14 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (11 11 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (11 11 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (11 11 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 )
(HSL-CLIENT-CH2-ON-HOME-GRANT
 (9814 216 (:REWRITE HIL-HSL-AND-HIL-AND-CH2-IMPLIES-HSL))
 (921 921 (:REWRITE DEFAULT-CAR))
 (920 920 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (920 920 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (920 920 (:REWRITE HSL-CH2-SET-REDUCTION))
 (920 920 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (920 920 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (920 920 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (920 920 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (920 920 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (920 920 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (920 920 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (820 820 (:REWRITE DEFAULT-CDR))
 (175 175 (:REWRITE HIL-HEG-SET-REDUCTION))
 (175 175 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (156 156 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (130 130 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (27 27 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 )
(|hsl-client-ch2 when home grants|
 (293 290 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (290 290 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (289 289 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (289 289 (:REWRITE HSL-CH2-SET-REDUCTION))
 (289 289 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (289 289 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (289 289 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (289 289 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (289 289 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (289 289 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (123 123 (:REWRITE DEFAULT-CAR))
 (122 122 (:REWRITE DEFAULT-CDR))
 (42 3 (:DEFINITION ALL-FALSE))
 (30 30 (:REWRITE HSL-CH3-AND-CH3-TO-HSL))
 (23 23 (:REWRITE HIL-HEG-SET-REDUCTION))
 (23 23 (:REWRITE CH2-EXCLUSIVE-MEANS-SET-IDLE))
 (19 19 (:REWRITE CH2-CLIENT-SHARED-IMPLIES-NOT-EXCLUSIVE))
 (18 18 (:REWRITE INVALIDATE-ACK-CH2-DOES-IT))
 (6 6 (:REWRITE CH2-EXCLUSIVE-AFTER-CH2-NIL))
 )
(INV)
(|inv holds in initial state|)
(|inv is inductive|
 (613 613 (:REWRITE HSL-HEG-HSL-CH3-IMPLIES-NONE))
 (613 613 (:REWRITE HSL-CH3-ALL-FALSE-TO-NOT-CH3))
 (613 613 (:REWRITE HSL-CH2-SET-REDUCTION))
 (613 613 (:REWRITE HSL-CH2-AND-ALL-FALSE-IMPLIES-NIL))
 (613 613 (:REWRITE HSL-CH2-AND-ALL-FALSE))
 (613 613 (:REWRITE HIL-HSL-AND-HIL-IMPLIES-HSL))
 (613 613 (:REWRITE HIL-HSL-AND-ALL-FALSE-TO-NOT-HIL))
 (613 613 (:REWRITE CHANNEL-NIL-FOR-EXCLUSIV-IMPLIES-NOT-ANYTHING-ELSE))
 (613 613 (:REWRITE CH2-EXCLUSIVE-MEANS-IDLE))
 (613 613 (:REWRITE ALL-FALSE-IMPLIES-FALSE))
 (4 4 (:REWRITE |heg exclusive home-grants-exclusive|))
 )
(|inv implies coherent|)
(GERMAN-RUN)
(|inv persists along run|
 (382 30 (:REWRITE |inv implies coherent|))
 (7 7 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE DEFAULT-CDR))
 )
(|inv is true of all runs from init|)
(|every run is coherent|)
