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(SETP-WHEN-NAT-SET-P)
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 (2 2 (:TYPE-PRESCRIPTION FAST-<<))
 )
(SETP-WHEN-NAT-SET-P)
(NATP-OF-HEAD-WHEN-NAT-SET-P
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 (60 8 (:REWRITE INTEGERP-OF-CAR-WHEN-INTEGER-LISTP))
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 (19 5 (:REWRITE <<-TRICHOTOMY))
 (17 3 (:REWRITE <<-ASYMMETRIC))
 (14 14 (:TYPE-PRESCRIPTION NAT-LISTP))
 (12 12 (:TYPE-PRESCRIPTION <<))
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 (10 10 (:REWRITE DEFAULT-CDR))
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 (8 4 (:REWRITE INTEGER-LISTP-OF-CDR-WHEN-INTEGER-LISTP))
 (5 5 (:REWRITE <<-TRANSITIVE))
 (4 4 (:TYPE-PRESCRIPTION FAST-<<))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE NAT-LISTP-OF-CDR-WHEN-NAT-LISTP))
 (4 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 )
(NAT-SET-P-OF-TAIL-WHEN-NAT-SET-P
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 (250 5 (:DEFINITION NAT-LISTP))
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 (57 15 (:REWRITE <<-TRICHOTOMY))
 (51 9 (:REWRITE <<-ASYMMETRIC))
 (46 7 (:REWRITE NAT-LISTP-OF-CDR-WHEN-NAT-LISTP))
 (40 40 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE INTEGER-LISTP-WHEN-NOT-CONSP))
 (15 15 (:REWRITE <<-TRANSITIVE))
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 (2 2 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 )
(NAT-SET-P-OF-INSERT
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 (231 35 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (223 27 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (215 187 (:REWRITE DEFAULT-CDR))
 (209 186 (:REWRITE DEFAULT-CAR))
 (206 10 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (198 164 (:REWRITE <<-TRANSITIVE))
 (198 8 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (152 120 (:REWRITE INTEGER-LISTP-WHEN-NOT-CONSP))
 (102 102 (:TYPE-PRESCRIPTION SET::SFIX$INLINE))
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 (64 48 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP))
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 (44 44 (:REWRITE DEFAULT-<-1))
 (36 18 (:REWRITE SET::IN-TAIL))
 (32 12 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (27 27 (:REWRITE SET::IN-TAIL-OR-HEAD))
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 (1 1 (:REWRITE <<-IRREFLEXIVE))
 )
(NATP-WHEN-IN-NAT-SET-P-BINDS-FREE-X
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(NOT-IN-NAT-SET-P-WHEN-NOT-NATP
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 )
(NAT-SET-P-OF-UNION
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 (64 34 (:REWRITE SET::TAIL-WHEN-EMPTYP))
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 (54 18 (:REWRITE SET::INTERSECT-EMPTYP-X))
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 (3 3 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
 (2 2 (:REWRITE SET::HEAD-UNIQUE))
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(NAT-SET-P-OF-DELETE
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 (90 12 (:REWRITE INTEGERP-OF-CAR-WHEN-INTEGER-LISTP))
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(NAT-SFIX
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(NAT-SET-P-OF-NAT-SFIX)
(NAT-SFIX-WHEN-NAT-SET-P
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(EMPTYP-NAT-SFIX
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(FTY::TMP-DEFFIXTYPE-IDEMPOTENT
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(NAT-SET-EQUIV$INLINE
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(NAT-SET-EQUIV-IS-AN-EQUIVALENCE)
(NAT-SET-EQUIV-IMPLIES-EQUAL-NAT-SFIX-1)
(NAT-SFIX-UNDER-NAT-SET-EQUIV)
(EQUAL-OF-NAT-SFIX-1-FORWARD-TO-NAT-SET-EQUIV)
(EQUAL-OF-NAT-SFIX-2-FORWARD-TO-NAT-SET-EQUIV)
(NAT-SET-EQUIV-OF-NAT-SFIX-1-FORWARD)
(NAT-SET-EQUIV-OF-NAT-SFIX-2-FORWARD)
(TMP-DEFTYPES-NATP-OF-NFIX)
(TMP-DEFTYPES-NFIX-WHEN-NATP
 (2 2 (:REWRITE DEFAULT-<-2))
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(NAT-SET-P)
(BOOLEANP-OFNAT-SET-P
 (4 2 (:DEFINITION NAT-SET-P))
 (2 2 (:TYPE-PRESCRIPTION FAST-<<))
 )
(SETP-WHEN-NAT-SET-P)
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 (8 4 (:REWRITE INTEGER-LISTP-OF-CDR-WHEN-INTEGER-LISTP))
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(NAT-SET-P-OF-TAIL-WHEN-NAT-SET-P
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(NATP-WHEN-IN-NAT-SET-P-BINDS-FREE-X
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(NAT-SET-P-OF-UNION
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(NAT-SET-P-OF-DELETE
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(NAT-SET-FIX
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(NAT-SET-P-OF-NAT-SET-FIX)
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(EMPTYP-NAT-SET-FIX
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(NAT-SEQUIV-IS-AN-EQUIVALENCE)
(NAT-SEQUIV-IMPLIES-EQUAL-NAT-SET-FIX-1)
(NAT-SET-FIX-UNDER-NAT-SEQUIV)
(EQUAL-OF-NAT-SET-FIX-1-FORWARD-TO-NAT-SEQUIV)
(EQUAL-OF-NAT-SET-FIX-2-FORWARD-TO-NAT-SEQUIV)
(NAT-SEQUIV-OF-NAT-SET-FIX-1-FORWARD)
(NAT-SEQUIV-OF-NAT-SET-FIX-2-FORWARD)
(TMP-DEFTYPES-NATP-OF-NFIX)
(TMP-DEFTYPES-NFIX-WHEN-NATP
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(NAT-SETP)
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(SETP-WHEN-NAT-SETP)
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 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 )
(INT-TERM-S-NUM->VAL-OF-INT-TERM-S-NUM
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 )
(INT-TERM-S-NUM-OF-FIELDS
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 (2 2 (:TYPE-PRESCRIPTION INT-TERM-S-P))
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 )
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 (2 2 (:TYPE-PRESCRIPTION INT-TERM-S-P))
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 )
(EQUAL-OF-INT-TERM-S-NUM
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 )
(INT-TERM-S-NUM-OF-IFIX-VAL)
(INT-TERM-S-NUM-INT-EQUIV-CONGRUENCE-ON-VAL)
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 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
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 (27 27 (:TYPE-PRESCRIPTION CONSP-OF-INT-TERM-S-FIX))
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 )
(INT-TERM-S-PLUS->ARGS$INLINE-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-PLUS->ARGS-WHEN-WRONG-KIND)
(INT-TERM-S-PLUS)
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 (1 1 (:REWRITE FTY::PROVE-EQUAL-OF-CONS-WHEN-FIRST-QUOTEP))
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(INT-TERM-S-PLUS-OF-INT-TERM-S-SET-FIX-ARGS)
(INT-TERM-S-PLUS-INT-TERM-S-SET-EQUIV-CONGRUENCE-ON-ARGS)
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 (3 3 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
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(INT-TERM-S-COUNT
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 (56 32 (:REWRITE DEFAULT-+-1))
 (56 4 (:DEFINITION LENGTH))
 (44 4 (:DEFINITION LEN))
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 (8 8 (:REWRITE DEFAULT-<-1))
 (8 4 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
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(INT-TERM-S-COUNT-FLAG
 (268 4 (:DEFINITION ACL2-COUNT))
 (92 32 (:REWRITE DEFAULT-+-2))
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 (44 4 (:DEFINITION LEN))
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 (8 8 (:REWRITE DEFAULT-<-1))
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(FLAG::FLAG-EQUIV-LEMMA)
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(RETURN-TYPE-OF-INT-TERM-S-COUNT.COUNT)
(RETURN-TYPE-OF-INT-TERM-S-SET-COUNT.COUNT)
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(INT-TERM-S-COUNT-OF-INT-TERM-S-FIX-X)
(INT-TERM-S-SET-COUNT-OF-INT-TERM-S-SET-FIX-X)
(INT-TERM-S-COUNT-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-SET-COUNT-INT-TERM-S-SET-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-COUNT-OF-INT-TERM-S-PLUS)
(INT-TERM-S-SET-COUNT-OF-INT-TERM-S-PLUS->ARGS)
(INT-TERM-S-SET-COUNT-WHEN-EMPTYP)
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(INT-TERM-S-SET-COUNT-OF-HEAD
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 (248 54 (:REWRITE DEFAULT-+-2))
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 (24 20 (:REWRITE SET::TAIL-WHEN-EMPTYP))
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(EVAL-INT-TERM-S
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 (16 4 (:REWRITE DEFAULT-+-2))
 (13 3 (:REWRITE DEFAULT-<-2))
 (9 3 (:REWRITE DEFAULT-<-1))
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 (16 4 (:REWRITE DEFAULT-+-2))
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 (9 3 (:REWRITE DEFAULT-<-1))
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 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
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(FLAG::FLAG-EQUIV-LEMMA)
(EVAL-INT-TERM-S/S-FLAG-EQUIVALENCES)
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(RETURN-TYPE-OF-EVAL-INT-TERM-S.I)
(RETURN-TYPE-OF-EVAL-INT-TERM-S-SET.I)
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 (8 1 (:REWRITE DEFAULT-+-1))
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 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
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(TMP-DEFTYPES-INTEGERP-OF-IFIX)
(TMP-DEFTYPES-IFIX-WHEN-INTEGERP)
(INT-TERM-S-P
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(INT-TERM-S-P-FLAG
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(FLAG::FLAG-EQUIV-LEMMA)
(INT-TERM-S-P-FLAG-EQUIVALENCES)
(CONSP-WHEN-INT-TERM-S-P)
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 (2 2 (:TYPE-PRESCRIPTION FAST-<<))
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(INT-TERM-S-P-OF-HEAD-WHEN-INT-TERM-S-SET-P
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 (32 4 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
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 (20 20 (:TYPE-PRESCRIPTION LEN))
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(INT-TERM-S-SET-P-OF-TAIL-WHEN-INT-TERM-S-SET-P
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 (22 22 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
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 (3 3 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
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 (51 9 (:REWRITE <<-ASYMMETRIC))
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 (15 15 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 (15 15 (:REWRITE <<-TRANSITIVE))
 (14 14 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (12 12 (:REWRITE DEFAULT-CDR))
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 (12 2 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (11 11 (:TYPE-PRESCRIPTION FAST-<<))
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 (9 3 (:REWRITE SET::DELETE-PRESERVES-EMPTYP))
 (8 4 (:REWRITE SET::IN-TAIL))
 (8 2 (:REWRITE SET::INSERT-IDENTITY))
 (6 6 (:TYPE-PRESCRIPTION SET::SFIX$INLINE))
 (6 6 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (6 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (5 5 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (5 5 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (4 2 (:REWRITE SET::DELETE-IN))
 (2 2 (:REWRITE SET::HEAD-UNIQUE))
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(INT-TERM-S-KIND$INLINE
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(INT-TERM-S-KIND-POSSIBILITIES)
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(FLAG::FLAG-EQUIV-LEMMA)
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 (8 8 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 (4 4 (:REWRITE TMP-DEFTYPES-IFIX-WHEN-INTEGERP))
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(RETURN-TYPE-OF-INT-TERM-S-FIX.NEW-X)
(INT-TERM-S-SET-P-OF-INT-TERM-S-SET-FIX)
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(EMPTYP-INT-TERM-S-SET-FIX
 (4 2 (:REWRITE INT-TERM-S-SET-FIX-WHEN-INT-TERM-S-SET-P))
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(EMPTYP-OF-INT-TERM-S-SET-FIX
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(FLAG-LEMMA-FOR-INT-TERM-S-FIX-WHEN-INT-TERM-S-P
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(INT-TERM-S-FIX-WHEN-INT-TERM-S-P)
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(FTY::TMP-DEFFIXTYPE-IDEMPOTENT
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 )
(INT-TERM-S-EQUIV$INLINE)
(INT-TERM-S-EQUIV-IS-AN-EQUIVALENCE)
(INT-TERM-S-EQUIV-IMPLIES-EQUAL-INT-TERM-S-FIX-1)
(INT-TERM-S-FIX-UNDER-INT-TERM-S-EQUIV)
(EQUAL-OF-INT-TERM-S-FIX-1-FORWARD-TO-INT-TERM-S-EQUIV)
(EQUAL-OF-INT-TERM-S-FIX-2-FORWARD-TO-INT-TERM-S-EQUIV)
(INT-TERM-S-EQUIV-OF-INT-TERM-S-FIX-1-FORWARD)
(INT-TERM-S-EQUIV-OF-INT-TERM-S-FIX-2-FORWARD)
(FTY::TMP-DEFFIXTYPE-IDEMPOTENT
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 )
(INT-TERM-S-SET-EQUIV$INLINE
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 )
(INT-TERM-S-SET-EQUIV-IS-AN-EQUIVALENCE)
(INT-TERM-S-SET-EQUIV-IMPLIES-EQUAL-INT-TERM-S-SET-FIX-1)
(INT-TERM-S-SET-FIX-UNDER-INT-TERM-S-SET-EQUIV)
(EQUAL-OF-INT-TERM-S-SET-FIX-1-FORWARD-TO-INT-TERM-S-SET-EQUIV)
(EQUAL-OF-INT-TERM-S-SET-FIX-2-FORWARD-TO-INT-TERM-S-SET-EQUIV)
(INT-TERM-S-SET-EQUIV-OF-INT-TERM-S-SET-FIX-1-FORWARD)
(INT-TERM-S-SET-EQUIV-OF-INT-TERM-S-SET-FIX-2-FORWARD)
(INT-TERM-S-KIND$INLINE-OF-INT-TERM-S-FIX-X
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 (7 5 (:REWRITE INT-TERM-S-SET-FIX-WHEN-INT-TERM-S-SET-P))
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 )
(INT-TERM-S-KIND$INLINE-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(CONSP-OF-INT-TERM-S-FIX)
(TAG-WHEN-INT-TERM-S-P-FORWARD
 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 )
(TAG-OF-INT-TERM-S-FIX)
(INT-TERM-S-NUM->VAL$INLINE
 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 )
(INTEGERP-OF-INT-TERM-S-NUM->VAL)
(INT-TERM-S-NUM->VAL$INLINE-OF-INT-TERM-S-FIX-X
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 )
(INT-TERM-S-NUM->VAL$INLINE-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-NUM->VAL-WHEN-WRONG-KIND
 (2 2 (:REWRITE TMP-DEFTYPES-IFIX-WHEN-INTEGERP))
 )
(INT-TERM-S-NUM)
(RETURN-TYPE-OF-INT-TERM-S-NUM
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 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 )
(INT-TERM-S-NUM->VAL-OF-INT-TERM-S-NUM
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 )
(INT-TERM-S-NUM-OF-FIELDS
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 )
(INT-TERM-S-FIX-WHEN-NUM
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 (2 2 (:TYPE-PRESCRIPTION INT-TERM-S-P))
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 )
(EQUAL-OF-INT-TERM-S-NUM
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 )
(INT-TERM-S-NUM-OF-IFIX-VAL)
(INT-TERM-S-NUM-INT-EQUIV-CONGRUENCE-ON-VAL)
(INT-TERM-S-PLUS->ARGS$INLINE
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 (1 1 (:REWRITE INT-TERM-S-P-WHEN-IN-INT-TERM-S-SET-P-BINDS-FREE-X))
 )
(INT-TERM-S-SET-P-OF-INT-TERM-S-PLUS->ARGS
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 )
(INT-TERM-S-PLUS->ARGS$INLINE-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-PLUS->ARGS-WHEN-WRONG-KIND)
(INT-TERM-S-PLUS)
(RETURN-TYPE-OF-INT-TERM-S-PLUS
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(INT-TERM-S-PLUS-OF-FIELDS
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 (4 1 (:REWRITE INT-TERM-S-FIX-WHEN-INT-TERM-S-P))
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(INT-TERM-S-FIX-WHEN-PLUS
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(EQUAL-OF-INT-TERM-S-PLUS
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 )
(INT-TERM-S-PLUS-OF-INT-TERM-S-SET-FIX-ARGS)
(INT-TERM-S-PLUS-INT-TERM-S-SET-EQUIV-CONGRUENCE-ON-ARGS)
(INT-TERM-S-FIX-REDEF
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(INT-TERM-S-COUNT
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(INT-TERM-S-COUNT-FLAG
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(FLAG::FLAG-EQUIV-LEMMA)
(INT-TERM-S-COUNT-FLAG-EQUIVALENCES)
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(RETURN-TYPE-OF-INT-TERM-S-COUNT.COUNT)
(RETURN-TYPE-OF-INT-TERM-S-SET-COUNT.COUNT)
(INT-TERM-S-COUNT
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(INT-TERM-S-COUNT-OF-INT-TERM-S-FIX-X)
(INT-TERM-S-SET-COUNT-OF-INT-TERM-S-SET-FIX-X)
(INT-TERM-S-COUNT-INT-TERM-S-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-SET-COUNT-INT-TERM-S-SET-EQUIV-CONGRUENCE-ON-X)
(INT-TERM-S-COUNT-OF-INT-TERM-S-PLUS)
(INT-TERM-S-SET-COUNT-OF-INT-TERM-S-PLUS->ARGS)
(INT-TERM-S-SET-COUNT-WHEN-EMPTYP)
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(REC-SET-P-FLAG
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(FLAG::FLAG-EQUIV-LEMMA)
(REC-SET-P-FLAG-EQUIVALENCES)
(CONSP-WHEN-REC-SET-P)
(BOOLEANP-OFREC-SET-SET-P
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(SETP-WHEN-REC-SET-SET-P
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(REC-SET-SET-P-OF-TAIL-WHEN-REC-SET-SET-P
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