(ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:TYPE-PRESCRIPTION MAYBE-EXPAND-ARRAY))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(NATP-OF-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (20 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (14 3 (:REWRITE DEFAULT-<-2))
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (8 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 3 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (3 3 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME-3
 (20 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (14 3 (:REWRITE DEFAULT-<-2))
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (9 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (6 3 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (4 3 (:REWRITE DEFAULT-<-1))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (3 3 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(PSEUDO-DAG-ARRAYP-OF-MV-NTH-2-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (430 430 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (95 27 (:REWRITE DEFAULT-<-2))
 (92 46 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (48 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (46 46 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (27 27 (:REWRITE USE-ALL-<-2))
 (27 27 (:REWRITE USE-ALL-<))
 (27 27 (:REWRITE DEFAULT-<-1))
 (25 25 (:TYPE-PRESCRIPTION NATP))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (20 20 (:REWRITE DEFAULT-+-2))
 (20 20 (:REWRITE DEFAULT-+-1))
 (16 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 1 (:LINEAR <-OF-ALEN1-OF-MAYBE-EXPAND-ARRAY-LINEAR))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 )
(NATP-OF-MV-NTH-1-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (20 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (14 3 (:REWRITE DEFAULT-<-2))
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (8 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(ARRAY1P-OF-MV-NTH-2-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (44 22 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (22 22 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (20 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (16 5 (:REWRITE DEFAULT-<-2))
 (8 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:LINEAR ARRAY2P-LINEAR))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME-2
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (27 4 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (17 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 4 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
(<=-OF-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (80 40 (:TYPE-PRESCRIPTION NATP-OF-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME))
 (42 42 (:TYPE-PRESCRIPTION NATP))
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (36 18 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (33 9 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (18 18 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (18 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 2 (:DEFINITION NATP))
 (10 1 (:LINEAR BOUND-ON-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME-3))
 (10 1 (:LINEAR BOUND-ON-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME-2))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(BOUND-ON-MV-NTH-3-AND-MV-NTH-1-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (100 5 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (68 11 (:REWRITE DEFAULT-<-2))
 (50 50 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (44 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 5 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (13 11 (:REWRITE DEFAULT-<-1))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (10 10 (:TYPE-PRESCRIPTION ARRAY1P))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 1 (:LINEAR <=-OF-MV-NTH-3-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE BOUNDED-DAG-VARIABLE-ALISTP-MONOTONE))
 )
(DAG-PARENT-ARRAYP-OF-MV-NTH-4-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (46 23 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (23 23 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (20 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (8 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (4 4 (:LINEAR ARRAY2P-LINEAR))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ALEN1-OF-MV-NTH-4-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (84 42 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (71 17 (:REWRITE DEFAULT-<-2))
 (42 42 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (42 13 (:REWRITE DEFAULT-CDR))
 (41 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (34 2 (:DEFINITION MIN))
 (20 5 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (19 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (16 4 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P))
 (13 2 (:REWRITE DEFAULT-*-2))
 (12 3 (:DEFINITION ASSOC-KEYWORD))
 (9 9 (:TYPE-PRESCRIPTION ASSOC-KEYWORD))
 (9 9 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P-FREE))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE DIMENSIONS-WHEN-NOT-CONSP-OF-HEADER-CHEAP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-*-1))
 )
(MV-NTH-5-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (21 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (12 1 (:REWRITE DEFAULT-<-2))
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (10 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 1 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(DAG-VARIABLE-ALISTP-OF-MV-NTH-6-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (20 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (14 3 (:REWRITE DEFAULT-<-2))
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (8 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(BOUNDED-DAG-VARIABLE-ALISTP-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (130 13 (:DEFINITION STRIP-CDRS))
 (104 26 (:REWRITE DEFAULT-CDR))
 (93 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (60 3 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (41 8 (:REWRITE DEFAULT-<-2))
 (39 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (30 30 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (24 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 8 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (13 13 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (13 13 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (13 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 3 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (10 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 4 (:REWRITE ALL-<-OF-STRIP-CDRS-OF-0-WHEN-DAG-VARIABLE-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION ARRAY1P))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE BOUNDED-DAG-VARIABLE-ALISTP-MONOTONE))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(BOUNDED-DAG-PARENT-ENTRIESP-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (176 88 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (104 68 (:REWRITE DEFAULT-<-2))
 (104 46 (:REWRITE DEFAULT-+-2))
 (88 88 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (86 68 (:REWRITE DEFAULT-<-1))
 (68 68 (:REWRITE USE-ALL-<-2))
 (68 68 (:REWRITE USE-ALL-<))
 (58 58 (:TYPE-PRESCRIPTION NATP))
 (46 46 (:REWRITE DEFAULT-+-1))
 (44 11 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (34 6 (:LINEAR <-OF-ALEN1-OF-MAYBE-EXPAND-ARRAY-LINEAR))
 (32 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (21 21 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (16 8 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (16 4 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (12 12 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (12 12 (:LINEAR ARRAY2P-LINEAR))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (6 6 (:REWRITE ALL-DAG-PARENT-ENTRIESP-MONOTONE-1))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 )
(BOUNDED-DAG-PARENT-ARRAYP-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (24 4 (:REWRITE DEFAULT-+-2))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (6 2 (:REWRITE ARRAY1P-OF-MV-NTH-2-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME))
 (5 4 (:REWRITE DEFAULT-<-2))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 )
(DAG-VARIABLE-ALIST-CORRECT-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (103 103 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (60 3 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (40 20 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (38 5 (:REWRITE DEFAULT-<-2))
 (24 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 20 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (12 3 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (6 6 (:TYPE-PRESCRIPTION ARRAY1P))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 )
(DAG-CONSTANT-ALIST-CORRECT-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (93 93 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (38 19 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (26 4 (:REWRITE DEFAULT-<-2))
 (19 19 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(DAG-CONSTANT-ALIST-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (93 93 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (38 19 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (26 4 (:REWRITE DEFAULT-<-2))
 (19 19 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(WF-DAGP-AFTER-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 )
(ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (122 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (60 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (53 1 (:DEFINITION NAT-LISTP))
 (34 1 (:DEFINITION NATP))
 (21 9 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (21 3 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (19 19 (:TYPE-PRESCRIPTION ALL-<))
 (19 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 12 (:LINEAR ARRAY2P-LINEAR))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (9 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 9 (:REWRITE ALL-<-TRANSITIVE))
 (9 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (3 3 (:TYPE-PRESCRIPTION MAYBE-EXPAND-ARRAY))
 (3 1 (:REWRITE DAG-VARIABLE-ALISTP-FORWARD-TO-ALIST))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 1 (:TYPE-PRESCRIPTION ADD-TO-PARENTS-OF-ATOMS-WITH-NAME))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
(NATP-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (74 1 (:REWRITE NATP-OF-LOOKUP-EQUAL-WHEN-NAT-LISTP-OF-STRIP-CDRS))
 (59 1 (:DEFINITION NAT-LISTP))
 (22 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (20 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (11 11 (:TYPE-PRESCRIPTION NAT-LISTP))
 (10 1 (:DEFINITION STRIP-CDRS))
 (9 7 (:REWRITE DEFAULT-<-2))
 (9 3 (:REWRITE DEFAULT-CDR))
 (9 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (6 3 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (4 1 (:REWRITE <-OF-LOOKUP-EQUAL-WHEN-BOUNDED-DAG-CONSTANT-ALISTP))
 (3 3 (:TYPE-PRESCRIPTION STRIP-CDRS))
 (3 3 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (3 3 (:TYPE-PRESCRIPTION ALL-<))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (3 1 (:REWRITE ALL-<-OF-STRIP-CDRS-OF-0-WHEN-DAG-VARIABLE-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-CONSTANT-ALISTP))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 (1 1 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(<-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-AND-0)
(DARGP-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (74 1 (:REWRITE NATP-OF-LOOKUP-EQUAL-WHEN-NAT-LISTP-OF-STRIP-CDRS))
 (59 1 (:DEFINITION NAT-LISTP))
 (22 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (20 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (11 11 (:TYPE-PRESCRIPTION NAT-LISTP))
 (10 1 (:DEFINITION STRIP-CDRS))
 (9 7 (:REWRITE DEFAULT-<-2))
 (9 3 (:REWRITE DEFAULT-CDR))
 (9 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (6 3 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (4 1 (:REWRITE <-OF-LOOKUP-EQUAL-WHEN-BOUNDED-DAG-CONSTANT-ALISTP))
 (3 3 (:TYPE-PRESCRIPTION STRIP-CDRS))
 (3 3 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (3 3 (:TYPE-PRESCRIPTION ALL-<))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (3 3 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (3 3 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (3 3 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (3 1 (:REWRITE ALL-<-OF-STRIP-CDRS-OF-0-WHEN-DAG-VARIABLE-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-CONSTANT-ALISTP))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE DARGP-OF-LOOKUP-EQUAL-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CDRS))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 (1 1 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(NOT-CONSP-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME)
(ARRAY1P-OF-MV-NTH-2-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (30 8 (:REWRITE DEFAULT-<-2))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(PSEUDO-DAG-ARRAYP-OF-MV-NTH-2-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (290 290 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (80 4 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (54 10 (:REWRITE DEFAULT-<-2))
 (49 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (32 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (18 18 (:REWRITE DEFAULT-+-2))
 (18 18 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (13 13 (:TYPE-PRESCRIPTION ALL-<))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE USE-ALL-<))
 (10 10 (:REWRITE DEFAULT-<-1))
 (7 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (2 2 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(NATP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (26 4 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (180 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (130 4 (:DEFINITION NAT-LISTP))
 (82 2 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (82 2 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (72 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (22 22 (:TYPE-PRESCRIPTION ALL-NATP))
 (22 4 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (16 8 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (14 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (8 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (4 4 (:LINEAR ARRAY2P-LINEAR))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (2 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(<-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-AND-0
 (2 1 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-2
 (64 32 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (27 4 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (17 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(<=-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (71 71 (:TYPE-PRESCRIPTION NATP))
 (70 35 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (70 35 (:TYPE-PRESCRIPTION NATP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (28 5 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (17 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 1 (:LINEAR BOUND-ON-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-2))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (6 1 (:DEFINITION NATP))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(BOUND-ON-MV-NTH-3-AND-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (154 77 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (117 71 (:TYPE-PRESCRIPTION NATP-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (70 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (54 8 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (30 5 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (20 17 (:REWRITE DEFAULT-<-2))
 (20 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (10 10 (:TYPE-PRESCRIPTION ALL-<))
 (10 10 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (10 10 (:LINEAR ARRAY2P-LINEAR))
 (10 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (10 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (9 9 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (5 5 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (5 5 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (5 5 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (5 5 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (5 5 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (5 5 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (5 1 (:LINEAR <=-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (4 4 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-3
 (80 4 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (76 38 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (51 7 (:REWRITE DEFAULT-<-2))
 (40 40 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (33 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (16 4 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (8 8 (:TYPE-PRESCRIPTION ARRAY1P))
 (8 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 1 (:LINEAR <=-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (4 4 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 1 (:LINEAR BOUND-ON-MV-NTH-3-AND-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-CONSTANT-ALISTP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-3-GEN
 (130 65 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (5 2 (:REWRITE DEFAULT-<-1))
 (5 1 (:LINEAR <=-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (4 1 (:LINEAR BOUND-ON-MV-NTH-3-AND-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-CONSTANT-ALISTP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 )
(ALEN1-OF-MV-NTH-4-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (140 32 (:REWRITE DEFAULT-<-2))
 (84 26 (:REWRITE DEFAULT-CDR))
 (82 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (68 4 (:DEFINITION MIN))
 (40 10 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (36 32 (:REWRITE DEFAULT-<-1))
 (32 32 (:REWRITE USE-ALL-<-2))
 (32 32 (:REWRITE USE-ALL-<))
 (32 8 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P))
 (26 4 (:REWRITE DEFAULT-*-2))
 (24 6 (:DEFINITION ASSOC-KEYWORD))
 (18 18 (:TYPE-PRESCRIPTION ASSOC-KEYWORD))
 (18 18 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (10 5 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P-FREE))
 (6 6 (:REWRITE DIMENSIONS-WHEN-NOT-CONSP-OF-HEADER-CHEAP))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (4 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(DAG-PARENT-ARRAYP-OF-MV-NTH-4-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (348 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (273 9 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (195 6 (:DEFINITION NAT-LISTP))
 (123 3 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (123 3 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (108 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (72 6 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (45 45 (:TYPE-PRESCRIPTION NAT-LISTP))
 (40 4 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (33 33 (:TYPE-PRESCRIPTION ALL-NATP))
 (33 6 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (33 3 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (30 30 (:TYPE-PRESCRIPTION ALL-<))
 (29 22 (:REWRITE DEFAULT-<-2))
 (25 22 (:REWRITE DEFAULT-<-1))
 (24 12 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (18 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (12 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (12 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (9 9 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 9 (:REWRITE ALL-<-TRANSITIVE))
 (7 7 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(DAG-CONSTANT-ALISTP-OF-MV-NTH-5-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (40 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (26 4 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(ALL-<-OF-STRIP-CDRS-OF-MV-NTH-5-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (385 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (213 6 (:DEFINITION NAT-LISTP))
 (174 3 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (132 3 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (120 6 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (117 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (112 34 (:REWRITE DEFAULT-CDR))
 (111 8 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (83 17 (:REWRITE DEFAULT-<-2))
 (60 60 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (48 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (45 45 (:TYPE-PRESCRIPTION NAT-LISTP))
 (45 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (39 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (33 33 (:TYPE-PRESCRIPTION ALL-NATP))
 (33 6 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (24 12 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (20 20 (:REWRITE DEFAULT-CAR))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (17 17 (:REWRITE DEFAULT-<-1))
 (16 8 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (13 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (13 13 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:TYPE-PRESCRIPTION ARRAY1P))
 (12 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (9 9 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (9 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (9 3 (:REWRITE ALL-<-OF-STRIP-CDRS-OF-0-WHEN-DAG-VARIABLE-ALISTP))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (3 3 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(BOUNDED-DAG-CONSTANT-ALISTP-OF-MV-NTH-5-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (392 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (213 6 (:DEFINITION NAT-LISTP))
 (174 3 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (132 3 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (120 12 (:DEFINITION STRIP-CDRS))
 (117 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (102 30 (:REWRITE DEFAULT-CDR))
 (58 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (45 45 (:TYPE-PRESCRIPTION NAT-LISTP))
 (45 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (36 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (33 33 (:TYPE-PRESCRIPTION ALL-NATP))
 (33 6 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (24 12 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (18 18 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (12 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (12 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 10 (:REWRITE USE-ALL-<))
 (12 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (10 6 (:REWRITE ALL-<-TRANSITIVE))
 (9 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (9 3 (:REWRITE ALL-<-OF-STRIP-CDRS-OF-0-WHEN-DAG-VARIABLE-ALISTP))
 (8 8 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (3 3 (:REWRITE BOUNDED-DAG-CONSTANT-ALISTP-MONOTONE))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 )
(MV-NTH-6-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (42 2 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (24 2 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (20 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 2 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(BOUNDED-DAG-PARENT-ENTRIESP-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (2295 24 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (1986 57 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1365 42 (:DEFINITION NAT-LISTP))
 (861 21 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (861 21 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (756 42 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (315 315 (:TYPE-PRESCRIPTION NAT-LISTP))
 (231 231 (:TYPE-PRESCRIPTION ALL-NATP))
 (231 42 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (217 131 (:REWRITE DEFAULT-+-2))
 (207 207 (:TYPE-PRESCRIPTION ALL-<))
 (204 194 (:REWRITE DEFAULT-<-2))
 (204 194 (:REWRITE DEFAULT-<-1))
 (194 194 (:REWRITE USE-ALL-<-2))
 (194 194 (:REWRITE USE-ALL-<))
 (168 84 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (141 21 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (131 131 (:REWRITE DEFAULT-+-1))
 (116 29 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (92 92 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (84 42 (:REWRITE USE-ALL-<-FOR-CAR))
 (84 42 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (84 42 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (84 42 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (84 42 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (84 42 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (69 69 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (64 64 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (57 57 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (57 57 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (57 57 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (57 57 (:REWRITE ALL-<-TRANSITIVE))
 (48 24 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (48 24 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (48 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (44 44 (:REWRITE USE-ALL-NATP-2))
 (44 44 (:REWRITE USE-ALL-NATP))
 (42 42 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (42 42 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (42 42 (:REWRITE DEFAULT-CDR))
 (42 42 (:REWRITE DEFAULT-CAR))
 (42 42 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (42 42 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (40 20 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (36 21 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (32 32 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (29 29 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (28 28 (:LINEAR ARRAY2P-LINEAR))
 (24 24 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (24 24 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (24 24 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (21 21 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (21 21 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (18 18 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (18 18 (:REWRITE ALL-DAG-PARENT-ENTRIESP-MONOTONE-1))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(BOUNDED-DAG-PARENT-ARRAYP-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (269 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (195 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (183 5 (:DEFINITION NAT-LISTP))
 (91 3 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (84 3 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (76 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (60 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (31 5 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (29 29 (:TYPE-PRESCRIPTION ALL-NATP))
 (27 5 (:REWRITE USE-ALL-<-FOR-CAR))
 (24 4 (:REWRITE DEFAULT-+-2))
 (23 23 (:TYPE-PRESCRIPTION ALL-<))
 (20 10 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (16 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (10 5 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (10 5 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (10 5 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (10 5 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (10 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (7 7 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (3 1 (:REWRITE ARRAY1P-OF-MV-NTH-2-OF-ADD-VARIABLE-TO-DAG-ARRAY-WITH-NAME))
 (3 1 (:REWRITE ARRAY1P-OF-MV-NTH-2-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE BOUNDED-DAG-PARENT-ENTRIESP-MONOTONE))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 )
(BOUND-ON-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-4
 (200 100 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (126 36 (:REWRITE DEFAULT-<-2))
 (82 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (62 36 (:REWRITE DEFAULT-<-1))
 (40 10 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (40 10 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (36 36 (:REWRITE USE-ALL-<-2))
 (36 36 (:REWRITE USE-ALL-<))
 (32 32 (:TYPE-PRESCRIPTION NATP))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (13 13 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 3 (:REWRITE INTEGERP-OF-ALEN1))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (4 4 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 (3 3 (:REWRITE INTEGERP-OF-ALEN1-GEN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-1-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (62 31 (:TYPE-PRESCRIPTION POSP-OF-MV-NTH-3-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME))
 (60 60 (:TYPE-PRESCRIPTION NATP))
 (44 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (22 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (17 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (16 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (8 8 (:TYPE-PRESCRIPTION ALL-<))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (2 2 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 )
(NOT-<-OF-ALEN1-OF-MV-NTH-2-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (99 11 (:REWRITE DEFAULT-<-2))
 (80 4 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (72 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (36 9 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (22 11 (:REWRITE DEFAULT-<-1))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(NOT-<-OF-ALEN1-OF-MV-NTH-2-OF-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME-2
 (197 21 (:REWRITE DEFAULT-<-2))
 (128 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (120 6 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (64 16 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (21 21 (:REWRITE USE-ALL-<-2))
 (21 21 (:REWRITE USE-ALL-<))
 (21 21 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(DAG-VARIABLE-ALIST-CORRECT-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (247 247 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (120 6 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (79 13 (:REWRITE DEFAULT-<-2))
 (48 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 12 (:TYPE-PRESCRIPTION ARRAY1P))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(DAG-VARIABLE-ALIST-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (150 150 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (80 4 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (51 7 (:REWRITE DEFAULT-<-2))
 (32 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 4 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (8 8 (:TYPE-PRESCRIPTION ARRAY1P))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (2 2 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 )
(DAG-CONSTANT-ALIST-CORRECT-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (170 170 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (120 6 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (75 9 (:REWRITE DEFAULT-<-2))
 (48 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (12 12 (:TYPE-PRESCRIPTION ARRAY1P))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE LOOKUP-EQUAL-WHEN-NOT-ASSOC-EQUAL-CHEAP))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE ADD-TO-PARENTS-OF-ATOMS-WITH-NAME-WHEN-ALL-CONSP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(WF-DAGP-AFTER-ADD-FUNCTION-CALL-EXPR-TO-DAG-ARRAY-WITH-NAME
 (16 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (4 4 (:TYPE-PRESCRIPTION ALL-<))
 (4 4 (:LINEAR ARRAY2P-LINEAR))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 )
(EMPTY-DAG-ARRAY-WITH-NAME)
(WF-DAGP-OF-EMPTY-DAG-ARRAY-WITH-NAME
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
(MV-NTH-1-OF-EMPTY-DAG-ARRAY-WITH-NAME
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
