(CUTPOINT)
(|pre implies cutpoint|)
(|exitpoint implies cutpoint|
 (1 1 (:REWRITE |pre implies cutpoint|))
 )
(ASSERTION)
(CUTPOINT-MEASURE
 (5 5 (:TYPE-PRESCRIPTION |clock fn is natp|))
 )
(|STEPS-TO-CUTPOINT-TAIL-arity-1-defpun-test|)
(|STEPS-TO-CUTPOINT-TAIL-arity-1-defpun-base|)
(|STEPS-TO-CUTPOINT-TAIL-arity-1-step|)
(|STEPS-TO-CUTPOINT-TAIL-arity-1-defpun-stn|
 (4 4 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(|STEPS-TO-CUTPOINT-TAIL-arity-1-defpun-fn|
 (12 12 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (5 5 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5 1 (:REWRITE O<=-O-FINP-DEF))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE O-INFP-O-FINP-O<=))
 (2 1 (:REWRITE AC-<))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|STEPS-TO-CUTPOINT-TAIL-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |STEPS-TO-CUTPOINT-TAIL-arity-1-defpun-stn|))
 )
(|STEPS-TO-CUTPOINT-TAIL-arity-1-DEF|)
(STEPS-TO-CUTPOINT-TAIL)
(STEPS-TO-CUTPOINT-TAIL-DEF
 (6 6 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE |pre implies cutpoint|))
 (1 1 (:REWRITE |exitpoint implies cutpoint|))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(STEPS-TO-CUTPOINT)
(STEP-FN-CUTPOINT)
(ASSERTION-IMPLIES-CUTPOINT)
(CUTPOINT-INDUCTION
 (3 3 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(CLOCK-FN-TAIL-INV
 (106 106 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (102 89 (:REWRITE DEFAULT-+-2))
 (90 89 (:REWRITE DEFAULT-+-1))
 (76 32 (:REWRITE FOLD-CONSTS-IN-+))
 (76 13 (:REWRITE ZP-OPEN))
 (48 12 (:REWRITE <-0-+-NEGATIVE-1))
 (45 3 (:REWRITE NATP-POSP))
 (35 11 (:REWRITE NATP-RW))
 (27 3 (:REWRITE POSP-RW))
 (20 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE DEFAULT-UNARY-MINUS))
 (12 3 (:REWRITE <-+-NEGATIVE-0-1))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(CLOCK-FN-IS-NATP
 (6 6 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (3 3 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 )
(CLOCK-FN-PROVIDE-EXITPOINT
 (24 4 (:DEFINITION RUN-FN))
 (12 4 (:REWRITE ZP-OPEN))
 (7 6 (:REWRITE DEFAULT-+-2))
 (7 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:DEFINITION CLOCK-FN-TAIL-DEF))
 (1 1 (:LINEAR |clock fn is minimal|))
 )
(CLOCK-FN-IS-MINIMAL
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (4 1 (:DEFINITION RUN-FN))
 (3 3 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:DEFINITION CLOCK-FN-TAIL-DEF))
 )
(PRE-S-IMPLIES-INV
 (10 2 (:REWRITE ZP-OPEN))
 (5 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(PRE-IMPLIES-ASSERTION
 (4 1 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (1 1 (:REWRITE |exitpoint implies cutpoint|))
 )
(STEPS-TO-CUTPOINT-TAIL-INV
 (392 60 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (302 30 (:DEFINITION ASSERTION))
 (106 106 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (102 89 (:REWRITE DEFAULT-+-2))
 (90 89 (:REWRITE DEFAULT-+-1))
 (76 32 (:REWRITE FOLD-CONSTS-IN-+))
 (76 13 (:REWRITE ZP-OPEN))
 (65 13 (:REWRITE |inv implies step-fn inv|))
 (60 60 (:TYPE-PRESCRIPTION ASSERTION))
 (60 60 (:REWRITE |pre implies cutpoint|))
 (60 60 (:REWRITE |exitpoint implies cutpoint|))
 (55 55 (:TYPE-PRESCRIPTION INV))
 (48 12 (:REWRITE <-0-+-NEGATIVE-1))
 (45 3 (:REWRITE NATP-POSP))
 (42 42 (:REWRITE |pre implies inv|))
 (42 42 (:REWRITE PRE-S-IMPLIES-INV))
 (35 11 (:REWRITE NATP-RW))
 (30 30 (:REWRITE PRE-IMPLIES-ASSERTION))
 (27 3 (:REWRITE POSP-RW))
 (20 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE DEFAULT-UNARY-MINUS))
 (12 3 (:REWRITE <-+-NEGATIVE-0-1))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(STEPS-TO-CUTPOINT-IS-ORDINAL
 (96 18 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (69 9 (:DEFINITION ASSERTION))
 (18 18 (:TYPE-PRESCRIPTION ASSERTION))
 (18 18 (:REWRITE |pre implies cutpoint|))
 (18 18 (:REWRITE |exitpoint implies cutpoint|))
 (10 2 (:REWRITE ZP-OPEN))
 (9 9 (:REWRITE PRE-IMPLIES-ASSERTION))
 (8 8 (:TYPE-PRESCRIPTION INV))
 (8 8 (:REWRITE |pre implies inv|))
 (8 8 (:REWRITE PRE-S-IMPLIES-INV))
 (4 1 (:REWRITE NATP-RW))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(STEPS-TO-CUTPOINT-IS-NATP
 (68 12 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (49 6 (:DEFINITION ASSERTION))
 (28 2 (:DEFINITION STEPS-TO-CUTPOINT-TAIL-DEF))
 (24 4 (:DEFINITION RUN-FN))
 (14 14 (:TYPE-PRESCRIPTION ASSERTION))
 (12 12 (:REWRITE |pre implies cutpoint|))
 (12 12 (:REWRITE |exitpoint implies cutpoint|))
 (12 4 (:REWRITE ZP-OPEN))
 (7 6 (:REWRITE DEFAULT-+-2))
 (7 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (6 6 (:TYPE-PRESCRIPTION INV))
 (6 6 (:REWRITE |pre implies inv|))
 (6 6 (:REWRITE PRE-S-IMPLIES-INV))
 (6 6 (:REWRITE PRE-IMPLIES-ASSERTION))
 (6 3 (:REWRITE NATP-RW))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(STEPS-TO-CUTPOINT-PROVIDE-CUTPOINT
 (81 14 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (58 7 (:DEFINITION ASSERTION))
 (36 5 (:DEFINITION RUN-FN))
 (28 2 (:DEFINITION STEPS-TO-CUTPOINT-TAIL-DEF))
 (19 5 (:REWRITE ZP-OPEN))
 (18 18 (:TYPE-PRESCRIPTION ASSERTION))
 (14 14 (:REWRITE |pre implies cutpoint|))
 (14 14 (:REWRITE |exitpoint implies cutpoint|))
 (8 7 (:REWRITE DEFAULT-+-2))
 (8 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:TYPE-PRESCRIPTION INV))
 (7 7 (:REWRITE |pre implies inv|))
 (7 7 (:REWRITE PRE-S-IMPLIES-INV))
 (7 7 (:REWRITE PRE-IMPLIES-ASSERTION))
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION OMEGA))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE NATP-RW))
 )
(STEPS-TO-CUTPOINT-IS-MINIMAL
 (68 12 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (49 6 (:DEFINITION ASSERTION))
 (28 2 (:DEFINITION STEPS-TO-CUTPOINT-TAIL-DEF))
 (24 4 (:DEFINITION RUN-FN))
 (14 14 (:TYPE-PRESCRIPTION ASSERTION))
 (12 12 (:REWRITE |pre implies cutpoint|))
 (12 12 (:REWRITE |exitpoint implies cutpoint|))
 (12 4 (:REWRITE ZP-OPEN))
 (11 4 (:REWRITE DEFAULT-<-2))
 (7 6 (:REWRITE DEFAULT-+-2))
 (7 6 (:REWRITE DEFAULT-+-1))
 (7 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (6 6 (:TYPE-PRESCRIPTION OMEGA))
 (6 6 (:TYPE-PRESCRIPTION INV))
 (6 6 (:REWRITE |pre implies inv|))
 (6 6 (:REWRITE PRE-S-IMPLIES-INV))
 (6 6 (:REWRITE PRE-IMPLIES-ASSERTION))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE NATP-RW))
 )
(EXITPOINT-IMPLIES-S=STEP-FN-EXITPOINT
 (20 20 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (1 1 (:LINEAR |clock fn is minimal|))
 )
(EXITPOINT-AND-ASSERTION-IMPLIES-POST
 (16 1 (:DEFINITION RUN-FN))
 (9 1 (:REWRITE ZP-OPEN))
 (4 4 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (4 4 (:TYPE-PRESCRIPTION CLOCK-FN-IS-NATP))
 (4 4 (:REWRITE |pre implies inv|))
 (4 4 (:REWRITE PRE-S-IMPLIES-INV))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE PRE-IMPLIES-ASSERTION))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CLOCK-FN-PROVIDE-EXITPOINT))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(EXECUTE-FN
 (4 4 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(EXECUTE-FN=RUN-FN
 (6 6 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(RUN-FN-+-REDUCTION
 (28 13 (:REWRITE ZP-OPEN))
 (20 19 (:REWRITE DEFAULT-+-2))
 (19 19 (:REWRITE DEFAULT-+-1))
 (8 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE NATP-RW))
 (4 4 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(NOT-EXITPOINT-IMPLIES-NOT-EXITPOINT-+CUTPOINT
 (41 41 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (31 13 (:REWRITE DEFAULT-+-2))
 (27 5 (:REWRITE ZP-OPEN))
 (21 4 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (16 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 6 (:REWRITE DEFAULT-<-2))
 (15 2 (:DEFINITION ASSERTION))
 (13 13 (:REWRITE DEFAULT-+-1))
 (13 3 (:REWRITE <-0-+-NEGATIVE-1))
 (9 9 (:META CANCEL_PLUS-LESSP-CORRECT))
 (9 6 (:REWRITE DEFAULT-<-1))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:TYPE-PRESCRIPTION ASSERTION))
 (4 1 (:REWRITE NATP-POSP))
 (2 2 (:TYPE-PRESCRIPTION INV))
 (2 2 (:REWRITE |pre implies inv|))
 (2 2 (:REWRITE |pre implies cutpoint|))
 (2 2 (:REWRITE PRE-S-IMPLIES-INV))
 (2 2 (:REWRITE PRE-IMPLIES-ASSERTION))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:LINEAR |clock fn is minimal|))
 (1 1 (:REWRITE POSP-RW))
 )
(CLOCK-FN-STEPS-TO-CUTPOINT
 (97 97 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (33 33 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (12 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 )
(CLOCK-FN-LARGER-THAN-STEPS-TO-CUTPOINT
 (71 71 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (41 41 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (15 6 (:REWRITE DEFAULT-+-2))
 (7 2 (:DEFINITION RUN-FN))
 (6 6 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 (3 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 )
(STEP-FN-RUN-FN-=-RUN-FN-1+
 (9 9 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE ZP-OPEN))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (3 3 (:REWRITE NATP-RW))
 (1 1 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(EXITPOINT-AND-NOT-EXITPOINT-IMPLIES-CUTPOINT
 (41 7 (:REWRITE ZP-OPEN))
 (40 8 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (28 4 (:DEFINITION ASSERTION))
 (16 12 (:REWRITE DEFAULT-+-2))
 (13 3 (:REWRITE <-0-+-NEGATIVE-1))
 (12 12 (:REWRITE DEFAULT-+-1))
 (11 11 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (8 8 (:TYPE-PRESCRIPTION ASSERTION))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 6 (:REWRITE |pre implies cutpoint|))
 (6 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE PRE-IMPLIES-ASSERTION))
 (3 3 (:TYPE-PRESCRIPTION INV))
 (3 3 (:REWRITE |pre implies inv|))
 (3 3 (:REWRITE PRE-S-IMPLIES-INV))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:LINEAR |clock fn is minimal|))
 (1 1 (:REWRITE NATP-RW))
 )
(EXITPOINT-AND-NOT-EXITPOINT-IMPLIES-NATP
 (27 5 (:REWRITE ZP-OPEN))
 (21 4 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (15 2 (:DEFINITION ASSERTION))
 (14 10 (:REWRITE DEFAULT-+-2))
 (13 3 (:REWRITE <-0-+-NEGATIVE-1))
 (11 11 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (10 10 (:REWRITE DEFAULT-+-1))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION ASSERTION))
 (4 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (2 2 (:TYPE-PRESCRIPTION INV))
 (2 2 (:REWRITE |pre implies inv|))
 (2 2 (:REWRITE |pre implies cutpoint|))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE PRE-S-IMPLIES-INV))
 (2 2 (:REWRITE PRE-IMPLIES-ASSERTION))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:LINEAR |clock fn is minimal|))
 (2 2 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 )
(<=-STEPS-IMPLIES-STEP-FN-CUTPOINT-NATP
 (193 5 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (121 121 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (85 63 (:REWRITE DEFAULT-+-2))
 (68 1 (:LINEAR CLOCK-FN-LARGER-THAN-STEPS-TO-CUTPOINT))
 (63 63 (:REWRITE DEFAULT-+-1))
 (38 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (21 3 (:REWRITE COMMUTATIVITY-2-OF-+))
 (20 20 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (20 20 (:REWRITE ZP-OPEN))
 (15 10 (:REWRITE DEFAULT-<-2))
 (14 8 (:REWRITE NATP-RW))
 (10 10 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE STEPS-TO-CUTPOINT-IS-NATP))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:LINEAR |clock fn is minimal|))
 )
(EXITPOINT-AND-NOT-EXITPOINT-IMPLIES-N-NATP
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(RUN-FN-STEP-FN-=-RUN-FN-1+
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE NATP-RW))
 )
(ASSERTION-IMPLIES-ASSERTION-STEP-FN
 (2037 2037 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (1423 62 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (694 136 (:REWRITE DEFAULT-<-2))
 (637 295 (:REWRITE DEFAULT-+-2))
 (504 153 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (298 148 (:META CANCEL_PLUS-LESSP-CORRECT))
 (275 50 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (234 96 (:REWRITE NATP-RW))
 (154 154 (:REWRITE DEFAULT-CDR))
 (83 83 (:REWRITE FOLD-CONSTS-IN-+))
 (79 79 (:REWRITE |pre implies inv|))
 (79 79 (:REWRITE PRE-S-IMPLIES-INV))
 (57 57 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (57 57 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (50 50 (:REWRITE |pre implies cutpoint|))
 (50 50 (:REWRITE |exitpoint implies cutpoint|))
 (50 15 (:REWRITE STEP-FN-RUN-FN-=-RUN-FN-1+))
 (49 49 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 (48 48 (:REWRITE PRE-IMPLIES-ASSERTION))
 (44 44 (:REWRITE STEPS-TO-CUTPOINT-IS-NATP))
 (24 24 (:LINEAR |clock fn is minimal|))
 (2 2 (:LINEAR CLOCK-FN-LARGER-THAN-STEPS-TO-CUTPOINT))
 )
(PRE-IMPLIES-CLOCK-FN-IS-NATP)
(ASSERTION-IMPLIES-EXITPOINT-EXISTS
 (136 10 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (110 20 (:REWRITE ASSERTION-IMPLIES-CUTPOINT))
 (84 24 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (71 15 (:REWRITE DEFAULT-<-2))
 (58 28 (:REWRITE DEFAULT-+-2))
 (58 22 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (31 15 (:REWRITE DEFAULT-<-1))
 (30 30 (:REWRITE DEFAULT-CDR))
 (23 16 (:REWRITE DEFAULT-UNARY-MINUS))
 (22 22 (:REWRITE |pre implies inv|))
 (22 22 (:REWRITE PRE-S-IMPLIES-INV))
 (20 20 (:REWRITE |pre implies cutpoint|))
 (20 20 (:REWRITE |exitpoint implies cutpoint|))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (13 9 (:LINEAR |clock fn is minimal|))
 (10 10 (:REWRITE PRE-IMPLIES-ASSERTION))
 (10 10 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (10 10 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (9 9 (:LINEAR CLOCK-FN-IS-MINIMAL))
 (4 4 (:REWRITE CLOCK-FN-PROVIDE-EXITPOINT))
 (1 1 (:REWRITE CLOCK-FN-IS-NATP))
 )
(ASSERTION-INVARIANT-OVER-CUTPOINTS
 (60 20 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (48 48 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (2 2 (:LINEAR |clock fn is minimal|))
 (1 1 (:REWRITE PRE-IMPLIES-ASSERTION))
 )
(CUTPOINT-MEASURE-IS-ORDINAL
 (74 74 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (18 4 (:REWRITE DEFAULT-+-1))
 (12 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 4 (:REWRITE DEFAULT-+-2))
 (8 2 (:REWRITE NATP-RW))
 (4 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 2 (:DEFINITION MV-NTH))
 (3 3 (:REWRITE PRE-IMPLIES-ASSERTION))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(CLOCK-FN-IS-LARGER-THAN-STEPS-TO-CUTPOINT
 (13 13 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (5 5 (:TYPE-PRESCRIPTION |clock fn is natp|))
 )
(CLOCK-FN--WITH-CUTPOINT
 (617 617 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (470 470 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (198 26 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (191 44 (:REWRITE DEFAULT-+-2))
 (67 4 (:REWRITE NATP-POSP))
 (61 22 (:REWRITE DEFAULT-<-2))
 (61 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (52 44 (:REWRITE DEFAULT-+-1))
 (47 11 (:REWRITE NATP-RW))
 (46 4 (:REWRITE POSP-RW))
 (32 22 (:REWRITE DEFAULT-<-1))
 (22 22 (:META CANCEL_PLUS-LESSP-CORRECT))
 (19 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (9 9 (:LINEAR |clock fn is minimal|))
 (7 7 (:REWRITE STEPS-TO-CUTPOINT-IS-NATP))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 3 (:REWRITE O-INFP->NEQ-0))
 (4 4 (:REWRITE |clock fn produces exitpoint|))
 (3 3 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 (3 1 (:REWRITE STEP-FN-RUN-FN-=-RUN-FN-1+))
 )
(CLOCK-FN-DECREASES-AUX
 (197 197 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (141 141 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (36 3 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (34 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (34 6 (:REWRITE DEFAULT-<-1))
 (23 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:LINEAR |clock fn is minimal|))
 (4 1 (:REWRITE NATP-RW))
 (2 2 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 (1 1 (:REWRITE STEPS-TO-CUTPOINT-IS-NATP))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(CLOCK-FN-IS-NATP-FOR-PRE-DESCENDANT
 (14 1 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (12 6 (:REWRITE DEFAULT-+-2))
 (12 6 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CLOCK-FN-PROVIDE-EXITPOINT))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(ASSERTION-IMPLIES-NATP
 (28 28 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(ASSERTION-IMPLIES-MEASURE-DECREASES
 (145 29 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (137 137 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (91 9 (:REWRITE DEFAULT-+-1))
 (63 3 (:REWRITE CLOCK-FN-STEPS-TO-CUTPOINT))
 (56 9 (:REWRITE DEFAULT-+-2))
 (53 11 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (8 4 (:REWRITE DEFAULT-<-2))
 (6 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 3 (:DEFINITION MV-NTH))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 3 (:REWRITE PRE-IMPLIES-ASSERTION))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:LINEAR |clock fn is minimal|))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (3 1 (:REWRITE AC-<))
 (2 1 (:REWRITE O-INFP-O-FINP-O<=))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 )
(|pre implies assertion|
 (32 29 (:TYPE-PRESCRIPTION ASSERTION-IMPLIES-NATP))
 (29 29 (:TYPE-PRESCRIPTION CLOCK-FN-IS-NATP))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(|assertion implies cutpoint|
 (1 1 (:REWRITE |pre implies assertion|))
 (1 1 (:REWRITE PRE-IMPLIES-ASSERTION))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(|exitpoint and assertion implies post|
 (1 1 (:REWRITE |pre implies assertion|))
 (1 1 (:REWRITE PRE-IMPLIES-ASSERTION))
 (1 1 (:LINEAR |clock fn is minimal|))
 (1 1 (:LINEAR CLOCK-FN-IS-MINIMAL))
 )
(|cutpoint measure is an ordinal|)
(|assertion and not exitpoint implies assertion|
 (100 20 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (48 48 (:TYPE-PRESCRIPTION |clock fn is natp|))
 (48 48 (:TYPE-PRESCRIPTION CLOCK-FN-IS-NATP))
 (16 16 (:TYPE-PRESCRIPTION STEPS-TO-CUTPOINT-IS-NATP))
 (11 3 (:REWRITE DEFAULT-+-2))
 (10 3 (:REWRITE DEFAULT-+-1))
 (8 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:LINEAR |clock fn is minimal|))
 (2 2 (:REWRITE |pre implies assertion|))
 (1 1 (:REWRITE PRE-IMPLIES-ASSERTION))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:LINEAR STEPS-TO-CUTPOINT-IS-MINIMAL))
 )
