(BITS-IS-BITS_ALT
 (104 4 (:DEFINITION EXPT))
 (48 12 (:REWRITE DEFAULT-*-2))
 (40 8 (:REWRITE COMMUTATIVITY-OF-+))
 (32 12 (:REWRITE DEFAULT-*-1))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (28 2 (:REWRITE MOD-DOES-NOTHING))
 (22 22 (:REWRITE DEFAULT-+-2))
 (22 22 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE FOLD-CONSTS-IN-+))
 (15 10 (:REWRITE DEFAULT-<-2))
 (13 10 (:REWRITE DEFAULT-<-1))
 (12 4 (:TYPE-PRESCRIPTION NATP-MOD-2))
 (10 2 (:REWRITE DEFAULT-UNARY-/))
 (8 4 (:TYPE-PRESCRIPTION NATP-MOD))
 (5 1 (:REWRITE BITS-WITH-INDICES-IN-THE-WRONG-ORDER))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:TYPE-PRESCRIPTION MOD))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-MOD))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 2 (:REWRITE UNICITY-OF-0))
 (3 1 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (3 1 (:REWRITE BITS_ALT-NEG))
 (3 1 (:REWRITE BITS-NEG))
 (2 2 (:DEFINITION FIX))
 )
(BITN-IS-BITN_ALT
 (8 4 (:REWRITE BVECP-BITN_ALT-0))
 (8 4 (:REWRITE BITN_ALT-NEG))
 (4 4 (:REWRITE NEG-BITN_ALT-2))
 (4 4 (:REWRITE NEG-BITN_ALT-1))
 (4 4 (:REWRITE NEG-BITN_ALT-0))
 (4 3 (:REWRITE DEFAULT-<-1))
 (4 1 (:REWRITE BITN-NEG))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 1 (:REWRITE BVECP-BITN-0))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE NEG-BITN-2))
 (1 1 (:REWRITE NEG-BITN-1))
 (1 1 (:REWRITE NEG-BITN-0))
 )
(BINARY-CAT_ALT-IS-BINARY-CAT
 (40 4 (:REWRITE BITS_ALT-TAIL))
 (28 20 (:REWRITE DEFAULT-+-2))
 (28 20 (:REWRITE DEFAULT-+-1))
 (26 2 (:DEFINITION EXPT))
 (20 4 (:REWRITE FOLD-CONSTS-IN-+))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (12 4 (:REWRITE BITS_ALT-NEG))
 (10 10 (:TYPE-PRESCRIPTION BITS_ALT-NONNEGATIVE-INTEGERP-TYPE))
 (10 4 (:REWRITE DEFAULT-*-2))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (8 8 (:TYPE-PRESCRIPTION BVECP))
 (8 4 (:REWRITE UNICITY-OF-0))
 (8 4 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE BITS_ALT-TAIL-2))
 (4 4 (:DEFINITION FIX))
 (2 2 (:REWRITE ZIP-OPEN))
 )
(MULCAT_ALT-IS-MULCAT
 (30 24 (:REWRITE DEFAULT-*-2))
 (30 24 (:REWRITE DEFAULT-*-1))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (12 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 )
(HALF-ADDER)
(ADD-2)
(FULL-ADDER)
(ADD-3)
(RC-CARRY
 (6 6 (:TYPE-PRESCRIPTION LOGAND-NATP))
 )
(RC-CARRY-IS-RC-CARRY_ALT
 (24 12 (:REWRITE BVECP-BITN_ALT-0))
 (23 23 (:REWRITE DEFAULT-+-2))
 (23 23 (:REWRITE DEFAULT-+-1))
 (18 6 (:REWRITE FOLD-CONSTS-IN-+))
 (14 12 (:REWRITE BITN_ALT-NEG))
 (12 12 (:TYPE-PRESCRIPTION BVECP))
 (12 12 (:REWRITE NEG-BITN_ALT-2))
 (12 12 (:REWRITE NEG-BITN_ALT-1))
 (12 12 (:REWRITE NEG-BITN_ALT-0))
 (6 3 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(RC-SUM)
(RC-SUM-IS-RC-SUM_ALT
 (183 3 (:DEFINITION RC-CARRY_ALT))
 (69 23 (:REWRITE FOLD-CONSTS-IN-+))
 (56 56 (:REWRITE DEFAULT-+-2))
 (56 56 (:REWRITE DEFAULT-+-1))
 (42 18 (:REWRITE BVECP-BITN_ALT-0))
 (26 18 (:REWRITE BITN_ALT-NEG))
 (24 24 (:TYPE-PRESCRIPTION BVECP))
 (18 18 (:REWRITE NEG-BITN_ALT-2))
 (18 18 (:REWRITE NEG-BITN_ALT-1))
 (18 18 (:REWRITE NEG-BITN_ALT-0))
 (18 6 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 )
(RIPPLE-CARRY)
(GEN
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 5 (:REWRITE DEFAULT-+-2))
 (6 2 (:REWRITE BVECP-BITN_ALT-0))
 (5 5 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE NEG-BITN_ALT-2))
 (2 2 (:REWRITE NEG-BITN_ALT-1))
 (2 2 (:REWRITE NEG-BITN_ALT-0))
 (2 2 (:REWRITE BITN_ALT-NEG))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(GEN-IS-GEN_ALT
 (74 26 (:REWRITE BVECP-BITN_ALT-0))
 (35 35 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE NEG-BITN_ALT-2))
 (26 26 (:REWRITE NEG-BITN_ALT-1))
 (26 26 (:REWRITE NEG-BITN_ALT-0))
 (26 26 (:REWRITE BITN_ALT-NEG))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 )
(PROP
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 5 (:REWRITE DEFAULT-+-2))
 (6 2 (:REWRITE BVECP-BITN_ALT-0))
 (5 5 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE NEG-BITN_ALT-2))
 (2 2 (:REWRITE NEG-BITN_ALT-1))
 (2 2 (:REWRITE NEG-BITN_ALT-0))
 (2 2 (:REWRITE BITN_ALT-NEG))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(PROP-IS-PROP_ALT
 (60 20 (:REWRITE BVECP-BITN_ALT-0))
 (35 35 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE DEFAULT-<-1))
 (20 20 (:REWRITE NEG-BITN_ALT-2))
 (20 20 (:REWRITE NEG-BITN_ALT-1))
 (20 20 (:REWRITE NEG-BITN_ALT-0))
 (20 20 (:REWRITE BITN_ALT-NEG))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 )
(BVECP-1-GEN)
(BVECP-1-PROP)
(GEN-VAL)
(GEN-VAL-COR1)
(GEN-VAL-COR2)
(GEN-SPECIAL-CASE)
(PROP-VAL)
(PROP-AS-LOGXOR)
(GEN-EXTEND)
(GEN-EXTEND-COR)
(PROP-EXTEND)
(BITS-SUM)
(BITS-SUM-SWALLOW)
(BITS-SUM-COR)
(BITS-SUM-3)
(BITS-SUM-PLUS-1)
(LOGAND-GEN-0)
(LOGAND-GEN-0-COR
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (22 11 (:TYPE-PRESCRIPTION LOGAND-NATP-2))
 (22 11 (:TYPE-PRESCRIPTION LOGAND-NATP))
 )
(GEN-PLUS
 (30 15 (:TYPE-PRESCRIPTION LOGAND-NATP))
 (15 15 (:TYPE-PRESCRIPTION NATP))
 )
(GEN-EXTEND-3
 (15 15 (:TYPE-PRESCRIPTION NATP))
 (15 15 (:TYPE-PRESCRIPTION LOGAND-NATP))
 )
(LOP)
(LOP-IS-LOP
 (274 124 (:REWRITE DEFAULT-UNARY-MINUS))
 (230 166 (:REWRITE DEFAULT-+-2))
 (224 166 (:REWRITE DEFAULT-+-1))
 (168 64 (:REWRITE BVECP-BITN_ALT-0))
 (92 64 (:REWRITE BITN_ALT-NEG))
 (64 64 (:REWRITE NEG-BITN_ALT-2))
 (64 64 (:REWRITE NEG-BITN_ALT-1))
 (64 64 (:REWRITE NEG-BITN_ALT-0))
 (63 21 (:REWRITE FOLD-CONSTS-IN-+))
 (36 36 (:REWRITE DEFAULT-<-2))
 (36 36 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(LOP-BNDS)
(LOP-THM-1
 (36 18 (:TYPE-PRESCRIPTION NATP-MOD))
 (18 18 (:TYPE-PRESCRIPTION INTEGERP-MOD))
 )
(LAMT)
(LAMT-IS-LAMT_ALT)
(LAMG
 (10 5 (:TYPE-PRESCRIPTION LOGAND-NATP))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 )
(LAMG-IS-LAMG_ALT)
(LAMZ)
(LAMZ-IS-LAMZ_ALT
 (122 4 (:REWRITE BITS_ALT-TAIL-2))
 (52 4 (:DEFINITION EXPT))
 (22 22 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (22 22 (:TYPE-PRESCRIPTION LOGNOT))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (20 4 (:REWRITE BITS_ALT-TAIL))
 (17 9 (:REWRITE DEFAULT-<-2))
 (13 9 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 4 (:REWRITE DEFAULT-*-2))
 (12 4 (:REWRITE COMMUTATIVITY-OF-+))
 (8 8 (:TYPE-PRESCRIPTION BVECP))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (4 4 (:REWRITE BITS_ALT-NEG))
 )
(LAM1)
(LAM1-IS-LAM1_ALT
 (138 10 (:REWRITE BITS_ALT-TAIL-2))
 (52 4 (:DEFINITION EXPT))
 (40 10 (:REWRITE BITS_ALT-TAIL))
 (29 21 (:REWRITE DEFAULT-<-2))
 (26 14 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (25 21 (:REWRITE DEFAULT-<-1))
 (24 24 (:TYPE-PRESCRIPTION LOGNOT))
 (22 22 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (22 14 (:REWRITE BITS_ALT-NEG))
 (20 20 (:REWRITE DEFAULT-+-2))
 (20 20 (:REWRITE DEFAULT-+-1))
 (12 12 (:TYPE-PRESCRIPTION BVECP))
 (12 4 (:REWRITE DEFAULT-*-2))
 (12 4 (:REWRITE COMMUTATIVITY-OF-+))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(LAM2)
(LAM2-IS-LAM2_ALT
 (198 12 (:REWRITE BITS_ALT-TAIL-2))
 (78 6 (:DEFINITION EXPT))
 (50 12 (:REWRITE BITS_ALT-TAIL))
 (41 29 (:REWRITE DEFAULT-<-2))
 (36 36 (:TYPE-PRESCRIPTION LOGNOT))
 (36 36 (:REWRITE DEFAULT-+-2))
 (36 36 (:REWRITE DEFAULT-+-1))
 (35 29 (:REWRITE DEFAULT-<-1))
 (34 18 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (32 32 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (32 32 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (26 18 (:REWRITE BITS_ALT-NEG))
 (18 6 (:REWRITE DEFAULT-*-2))
 (16 16 (:TYPE-PRESCRIPTION BVECP))
 (6 6 (:REWRITE ZIP-OPEN))
 (6 6 (:REWRITE DEFAULT-*-1))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(LAM3)
(LAM3-IS-LAM3_ALT
 (138 10 (:REWRITE BITS_ALT-TAIL-2))
 (52 4 (:DEFINITION EXPT))
 (40 10 (:REWRITE BITS_ALT-TAIL))
 (33 25 (:REWRITE DEFAULT-<-2))
 (32 16 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (30 30 (:REWRITE DEFAULT-+-2))
 (30 30 (:REWRITE DEFAULT-+-1))
 (29 25 (:REWRITE DEFAULT-<-1))
 (24 24 (:TYPE-PRESCRIPTION LOGNOT))
 (24 16 (:REWRITE BITS_ALT-NEG))
 (22 22 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (12 12 (:TYPE-PRESCRIPTION BVECP))
 (12 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(LAM4)
(LAM4-IS-LAM4_ALT
 (78 8 (:REWRITE BITS_ALT-TAIL-2))
 (30 8 (:REWRITE BITS_ALT-TAIL))
 (26 2 (:DEFINITION EXPT))
 (24 12 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (21 17 (:REWRITE DEFAULT-<-2))
 (20 12 (:REWRITE BITS_ALT-NEG))
 (19 17 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE DEFAULT-+-2))
 (14 14 (:REWRITE DEFAULT-+-1))
 (12 12 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (12 12 (:TYPE-PRESCRIPTION LOGNOT))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (8 8 (:TYPE-PRESCRIPTION BVECP))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE DEFAULT-*-2))
 (6 2 (:REWRITE COMMUTATIVITY-OF-+))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE ZIP-OPEN))
 (2 2 (:REWRITE DEFAULT-*-1))
 )
(LAM0)
(LAM0-IS-LAM0_ALT
 (864 40 (:REWRITE BITS_ALT-TAIL-2))
 (416 24 (:DEFINITION EXPT))
 (160 40 (:REWRITE BITS_ALT-TAIL))
 (148 148 (:REWRITE DEFAULT-+-2))
 (148 148 (:REWRITE DEFAULT-+-1))
 (136 136 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (136 136 (:TYPE-PRESCRIPTION LOGNOT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (134 86 (:REWRITE DEFAULT-<-2))
 (110 86 (:REWRITE DEFAULT-<-1))
 (108 60 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (96 32 (:REWRITE DEFAULT-*-2))
 (76 60 (:REWRITE BITS_ALT-NEG))
 (48 48 (:TYPE-PRESCRIPTION BVECP))
 (32 32 (:REWRITE DEFAULT-*-1))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE ZIP-OPEN))
 )
(LAMB)
(LAMB-IS-LAMB
 (924 42 (:REWRITE BITS_ALT-TAIL-2))
 (512 32 (:DEFINITION EXPT))
 (240 176 (:REWRITE DEFAULT-+-2))
 (228 176 (:REWRITE DEFAULT-+-1))
 (228 2 (:REWRITE NEG-BITN_ALT-2))
 (202 202 (:TYPE-PRESCRIPTION LOGNOT))
 (198 198 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (198 198 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (174 110 (:REWRITE DEFAULT-<-2))
 (172 42 (:REWRITE DEFAULT-*-2))
 (170 42 (:REWRITE BITS_ALT-TAIL))
 (150 18 (:TYPE-PRESCRIPTION LOGIOR-NATP))
 (146 110 (:REWRITE DEFAULT-<-1))
 (132 48 (:TYPE-PRESCRIPTION LOGAND-NATP-2))
 (110 62 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (84 84 (:TYPE-PRESCRIPTION BITS_ALT-NONNEGATIVE-INTEGERP-TYPE))
 (78 62 (:REWRITE BITS_ALT-NEG))
 (60 60 (:TYPE-PRESCRIPTION BVECP))
 (42 42 (:REWRITE DEFAULT-*-1))
 (22 2 (:REWRITE NEG-BITN_ALT-0))
 (18 6 (:REWRITE DEFAULT-UNARY-MINUS))
 (18 2 (:REWRITE NEG-BITN_ALT-1))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE ZIP-OPEN))
 (6 2 (:REWRITE BVECP-BITN_ALT-0))
 (6 2 (:REWRITE BITN_ALT-BVECP-1))
 (4 4 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (2 2 (:REWRITE BITN_ALT-NEG))
 )
(LOP-THM-2
 (11 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(TOP-THM-1)
(TOP-THM-2)
