(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))
 )
(THETA)
(THETA-IS-THETA_ALT
 (24 12 (:REWRITE DEFAULT-+-2))
 (22 22 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (20 12 (:REWRITE DEFAULT-+-1))
 (18 6 (:REWRITE BVECP-BITN_ALT-0))
 (18 6 (:REWRITE BITN_ALT-NEG))
 (12 12 (:TYPE-PRESCRIPTION BVECP))
 (12 8 (:REWRITE DEFAULT-*-2))
 (8 8 (:REWRITE DEFAULT-*-1))
 (6 6 (:REWRITE NEG-BITN_ALT-2))
 (6 6 (:REWRITE NEG-BITN_ALT-1))
 (6 6 (:REWRITE NEG-BITN_ALT-0))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(SUM-THETA)
(SUM-THETA-IS-SUM-THETA_ALT
 (296 148 (:REWRITE DEFAULT-+-2))
 (266 148 (:REWRITE DEFAULT-+-1))
 (180 180 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (174 96 (:REWRITE DEFAULT-*-2))
 (168 6 (:DEFINITION EXPT))
 (156 96 (:REWRITE DEFAULT-*-1))
 (108 108 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (108 108 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (54 18 (:REWRITE BVECP-BITN_ALT-0))
 (42 18 (:REWRITE BITN_ALT-NEG))
 (36 36 (: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 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE ZIP-OPEN))
 )
(SUM-THETA-LEMMA)
(BMUX4)
(BMUX4-IS-BMUX4_ALT
 (136 4 (:REWRITE BITS_ALT-TAIL-2))
 (64 4 (:DEFINITION EXPT))
 (40 4 (:REWRITE BITS_ALT-TAIL))
 (32 8 (:REWRITE FOLD-CONSTS-IN-+))
 (24 24 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (24 24 (:REWRITE DEFAULT-+-2))
 (24 24 (:REWRITE DEFAULT-+-1))
 (24 4 (:REWRITE COMMUTATIVITY-OF-+))
 (20 20 (:TYPE-PRESCRIPTION LOGNOT))
 (18 10 (:REWRITE DEFAULT-<-2))
 (16 8 (:REWRITE DEFAULT-*-2))
 (14 10 (:REWRITE DEFAULT-<-1))
 (8 8 (:TYPE-PRESCRIPTION BVECP))
 (8 8 (:REWRITE DEFAULT-*-1))
 (8 4 (:REWRITE UNICITY-OF-0))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (4 4 (:REWRITE BITS_ALT-NEG))
 (4 4 (:DEFINITION FIX))
 )
(PP4
 (2 2 (:TYPE-PRESCRIPTION BMUX4))
 )
(PP4-IS-PP4_ALT
 (670 4 (:REWRITE NEG-BITN_ALT-2))
 (344 26 (:DEFINITION EXPT))
 (280 8 (:REWRITE BITS_ALT-TAIL-2))
 (201 165 (:REWRITE DEFAULT-+-2))
 (184 184 (:TYPE-PRESCRIPTION LOGNOT))
 (165 165 (:REWRITE DEFAULT-+-1))
 (125 73 (:REWRITE DEFAULT-<-2))
 (113 73 (:REWRITE DEFAULT-<-1))
 (106 54 (:REWRITE DEFAULT-*-2))
 (102 26 (:REWRITE COMMUTATIVITY-OF-+))
 (80 8 (:REWRITE BITS_ALT-TAIL))
 (54 54 (:REWRITE DEFAULT-*-1))
 (54 18 (:REWRITE DEFAULT-UNARY-MINUS))
 (44 4 (:REWRITE NEG-BITN_ALT-0))
 (36 4 (:REWRITE NEG-BITN_ALT-1))
 (12 4 (:REWRITE BVECP-BITN_ALT-0))
 (12 4 (:REWRITE BITN_ALT-BVECP-1))
 (8 8 (:REWRITE ZIP-OPEN))
 (8 8 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (8 8 (:REWRITE BITS_ALT-NEG))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE BITN_ALT-NEG))
 )
(SUM-PP4)
(SUM-PP4-IS-SUM-PP4_ALT
 (35 27 (:REWRITE DEFAULT-+-2))
 (35 27 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (8 8 (:TYPE-PRESCRIPTION PP4_ALT))
 (8 8 (:REWRITE ZP-OPEN))
 )
(BOOTH4-THM
 (149 97 (:REWRITE DEFAULT-+-2))
 (139 97 (:REWRITE DEFAULT-+-1))
 (101 45 (:REWRITE DEFAULT-*-2))
 (53 45 (:REWRITE DEFAULT-*-1))
 (48 24 (:REWRITE FOLD-CONSTS-IN-+))
 (22 19 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE DEFAULT-<-2))
 (12 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 8 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(PP4-THETA
 (2 2 (:TYPE-PRESCRIPTION BMUX4))
 )
(PP4-THETA-IS-PP4-THETA_ALT
 (882 34 (:REWRITE NEG-BITN_ALT-2))
 (324 24 (:DEFINITION EXPT))
 (298 250 (:REWRITE DEFAULT-<-2))
 (293 213 (:REWRITE DEFAULT-+-2))
 (286 250 (:REWRITE DEFAULT-<-1))
 (280 8 (:REWRITE BITS_ALT-TAIL-2))
 (241 213 (:REWRITE DEFAULT-+-1))
 (178 34 (:REWRITE NEG-BITN_ALT-0))
 (144 86 (:REWRITE DEFAULT-*-2))
 (120 120 (:TYPE-PRESCRIPTION LOGNOT))
 (102 34 (:REWRITE BVECP-BITN_ALT-0))
 (96 24 (:REWRITE COMMUTATIVITY-OF-+))
 (86 86 (:REWRITE DEFAULT-*-1))
 (86 34 (:REWRITE NEG-BITN_ALT-1))
 (80 8 (:REWRITE BITS_ALT-TAIL))
 (54 18 (:DEFINITION NATP))
 (48 16 (:REWRITE DEFAULT-UNARY-MINUS))
 (24 8 (:REWRITE BITN_ALT-BVECP-1))
 (18 18 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:REWRITE ZIP-OPEN))
 (8 8 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (8 8 (:REWRITE BITS_ALT-NEG))
 (1 1 (:REWRITE ZP-OPEN))
 )
(SUM-PP4-THETA)
(SUM-PP4-THETA-IS-SUM-PP4_ALT-THETA_ALT
 (4904 136 (:REWRITE NEG-BITN_ALT-2))
 (2536 184 (:DEFINITION EXPT))
 (1800 136 (:REWRITE NEG-BITN_ALT-0))
 (1707 1331 (:REWRITE DEFAULT-+-2))
 (1536 1248 (:REWRITE DEFAULT-<-2))
 (1467 1331 (:REWRITE DEFAULT-+-1))
 (1416 1248 (:REWRITE DEFAULT-<-1))
 (1120 32 (:REWRITE BITS_ALT-TAIL-2))
 (816 456 (:REWRITE DEFAULT-*-2))
 (600 600 (:TYPE-PRESCRIPTION LOGNOT))
 (456 456 (:REWRITE DEFAULT-*-1))
 (408 136 (:REWRITE BVECP-BITN_ALT-0))
 (344 136 (:REWRITE NEG-BITN_ALT-1))
 (336 112 (:REWRITE DEFAULT-UNARY-MINUS))
 (320 32 (:REWRITE BITS_ALT-TAIL))
 (136 56 (:DEFINITION NATP))
 (96 32 (:REWRITE BITN_ALT-BVECP-1))
 (80 80 (:REWRITE ZIP-OPEN))
 (56 56 (:TYPE-PRESCRIPTION NATP))
 (32 32 (:TYPE-PRESCRIPTION CAT_ALT-NONNEGATIVE-INTEGER-TYPE))
 (32 32 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (32 32 (:REWRITE BITS_ALT-NEG))
 (13 13 (:REWRITE ZP-OPEN))
 )
(BOOTH4-COROLLARY
 (2936 2 (:DEFINITION SUM-PP4_ALT-THETA_ALT))
 (2904 2 (:DEFINITION PP4_ALT-THETA_ALT))
 (2074 10 (:DEFINITION THETA_ALT))
 (1272 32 (:REWRITE NEG-BITN_ALT-2))
 (452 368 (:REWRITE DEFAULT-+-2))
 (428 32 (:REWRITE NEG-BITN_ALT-0))
 (406 368 (:REWRITE DEFAULT-+-1))
 (320 260 (:REWRITE DEFAULT-<-2))
 (286 260 (:REWRITE DEFAULT-<-1))
 (284 4 (:DEFINITION BMUX4_ALT))
 (266 136 (:REWRITE DEFAULT-*-2))
 (250 94 (:REWRITE FOLD-CONSTS-IN-+))
 (188 188 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (140 28 (:REWRITE DISTRIBUTIVITY))
 (140 4 (:REWRITE BITS_ALT-TAIL-2))
 (136 136 (:REWRITE DEFAULT-*-1))
 (88 32 (:REWRITE BVECP-BITN_ALT-0))
 (78 26 (:REWRITE DEFAULT-UNARY-MINUS))
 (70 70 (:TYPE-PRESCRIPTION LOGNOT))
 (56 28 (:REWRITE BITN_ALT-NEG))
 (56 6 (:DEFINITION NEG))
 (48 32 (:REWRITE NEG-BITN_ALT-1))
 (46 6 (:REWRITE COMMUTATIVITY-2-OF-+))
 (40 4 (:REWRITE BITS_ALT-TAIL))
 (36 12 (:REWRITE UNICITY-OF-0))
 (34 14 (:DEFINITION NATP))
 (32 32 (:REWRITE ZIP-OPEN))
 (24 12 (:DEFINITION FIX))
 (18 6 (:REWRITE BITN_ALT-BVECP-1))
 (16 2 (:REWRITE CAT_ALT-0))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (12 2 (:REWRITE CAT_ALT-BVECP))
 (8 8 (:TYPE-PRESCRIPTION CAT_ALT-NONNEGATIVE-INTEGER-TYPE))
 (4 4 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (4 4 (:REWRITE BITS_ALT-NEG))
 (2 2 (:REWRITE ZP-OPEN))
 )
(MU
 (98 98 (:REWRITE DEFAULT-CAR))
 (46 46 (:REWRITE DEFAULT-CDR))
 (18 12 (:REWRITE DEFAULT-<-1))
 (17 12 (:REWRITE DEFAULT-<-2))
 (11 11 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 2 (:DEFINITION POSP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 )
(MU-CHI
 (76 76 (:REWRITE DEFAULT-CAR))
 (37 37 (:REWRITE DEFAULT-CDR))
 (14 10 (:REWRITE DEFAULT-<-1))
 (13 10 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 1 (:DEFINITION POSP))
 (3 1 (:DEFINITION NATP))
 )
(MU-CHI-IS
 (234 134 (:REWRITE DEFAULT-+-2))
 (216 134 (:REWRITE DEFAULT-+-1))
 (145 69 (:REWRITE DEFAULT-<-1))
 (102 42 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (78 66 (:REWRITE DEFAULT-*-2))
 (75 25 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (69 69 (:REWRITE DEFAULT-<-2))
 (66 66 (:REWRITE DEFAULT-*-1))
 (49 25 (:REWRITE BITS_ALT-NEG))
 (39 24 (:REWRITE ZP-OPEN))
 )
(MU-CHI-IS-2
 (234 134 (:REWRITE DEFAULT-+-2))
 (216 134 (:REWRITE DEFAULT-+-1))
 (145 69 (:REWRITE DEFAULT-<-1))
 (102 42 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (78 66 (:REWRITE DEFAULT-*-2))
 (75 25 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (69 69 (:REWRITE DEFAULT-<-2))
 (66 66 (:REWRITE DEFAULT-*-1))
 (49 25 (:REWRITE BITS_ALT-NEG))
 (39 24 (:REWRITE ZP-OPEN))
 )
(MU-IS-MU)
(CHI-IS-CHI)
(PHI)
(PHI-IS-PHI_ALT
 (64 4 (:REWRITE BITS_ALT-TAIL-2))
 (40 4 (:DEFINITION CHI_ALT))
 (36 24 (:REWRITE DEFAULT-<-1))
 (36 24 (:REWRITE DEFAULT-+-2))
 (36 24 (:REWRITE DEFAULT-+-1))
 (32 32 (:TYPE-PRESCRIPTION CHI_ALT))
 (28 12 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (28 12 (:REWRITE BITS_ALT-NEG))
 (24 24 (:REWRITE DEFAULT-<-2))
 (24 16 (:REWRITE DEFAULT-*-2))
 (16 16 (:TYPE-PRESCRIPTION MU_ALT))
 (16 16 (:REWRITE DEFAULT-*-1))
 (12 4 (:REWRITE BITS_ALT-TAIL))
 (8 8 (:TYPE-PRESCRIPTION BVECP))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (4 4 (:REWRITE ZP-OPEN))
 )
(PHI-BND)
(CHI-M
 (10 1 (:DEFINITION CHI_ALT))
 (4 4 (:TYPE-PRESCRIPTION MU_ALT))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(PHI-M-1)
(SUM-PHI)
(SUM-PHI-IS-SUM-PHI_ALT
 (168 6 (:DEFINITION EXPT))
 (92 70 (:REWRITE DEFAULT-+-2))
 (92 70 (:REWRITE DEFAULT-+-1))
 (60 30 (:REWRITE DEFAULT-*-2))
 (42 30 (:REWRITE DEFAULT-*-1))
 (36 12 (:REWRITE FOLD-CONSTS-IN-+))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (18 18 (:TYPE-PRESCRIPTION PHI_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE ZIP-OPEN))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 )
(SUM-PHI-LEMMA)
(PP4-PHI
 (2 2 (:TYPE-PRESCRIPTION BMUX4))
 )
(PP4-PHI-IS-PP4_ALT-PHI_ALT
 (896 8 (:REWRITE NEG-BITN_ALT-2))
 (288 24 (:DEFINITION EXPT))
 (249 197 (:REWRITE DEFAULT-+-2))
 (224 224 (:TYPE-PRESCRIPTION LOGNOT))
 (200 200 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (200 200 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (197 197 (:REWRITE DEFAULT-+-1))
 (140 88 (:REWRITE DEFAULT-<-1))
 (136 88 (:REWRITE DEFAULT-<-2))
 (118 65 (:REWRITE DEFAULT-*-2))
 (88 8 (:REWRITE NEG-BITN_ALT-0))
 (72 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (72 24 (:REWRITE COMMUTATIVITY-OF-+))
 (72 8 (:REWRITE NEG-BITN_ALT-1))
 (65 65 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE BVECP-BITN_ALT-0))
 (24 8 (:REWRITE BITN_ALT-BVECP-1))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE BITN_ALT-NEG))
 )
(SUM-PP4-PHI)
(SUM-PP4-PHI-IS-SUM-PP4_ALT-PHI_ALT
 (22 16 (:REWRITE DEFAULT-+-2))
 (22 16 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION PP4_ALT-PHI_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 )
(STATIC-BOOTH
 (2418 2 (:DEFINITION SUM-PP4_ALT-PHI_ALT))
 (2386 2 (:DEFINITION PP4_ALT-PHI_ALT))
 (1010 10 (:DEFINITION PHI_ALT))
 (700 20 (:DEFINITION MU_ALT))
 (532 44 (:REWRITE BITS_ALT-TAIL-2))
 (492 4 (:DEFINITION BMUX4_ALT))
 (452 4 (:REWRITE NEG-BITN_ALT-2))
 (404 322 (:REWRITE DEFAULT-+-2))
 (382 322 (:REWRITE DEFAULT-+-1))
 (232 80 (:REWRITE FOLD-CONSTS-IN-+))
 (192 192 (:TYPE-PRESCRIPTION BITS_ALT-NONNEGATIVE-INTEGERP-TYPE))
 (188 44 (:REWRITE BITS_ALT-TAIL))
 (184 116 (:REWRITE DEFAULT-*-2))
 (181 129 (:REWRITE DEFAULT-<-1))
 (170 34 (:REWRITE DISTRIBUTIVITY))
 (161 129 (:REWRITE DEFAULT-<-2))
 (150 150 (:TYPE-PRESCRIPTION LOGNOT))
 (116 116 (:REWRITE DEFAULT-*-1))
 (88 8 (:REWRITE BITS_ALT-BITS_ALT))
 (80 56 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (72 72 (:TYPE-PRESCRIPTION MU_ALT))
 (68 2 (:DEFINITION SUM-ODD-POWERS-OF-2))
 (64 56 (:REWRITE BITS_ALT-NEG))
 (54 6 (:DEFINITION NEG))
 (44 4 (:REWRITE NEG-BITN_ALT-0))
 (40 40 (:TYPE-PRESCRIPTION CHI_ALT))
 (40 16 (:REWRITE UNICITY-OF-0))
 (36 4 (:REWRITE NEG-BITN_ALT-1))
 (24 16 (:DEFINITION FIX))
 (24 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (24 4 (:REWRITE COMMUTATIVITY-2-OF-+))
 (16 16 (:REWRITE ZIP-OPEN))
 (16 2 (:REWRITE CAT_ALT-0))
 (12 4 (:REWRITE BVECP-BITN_ALT-0))
 (12 4 (:REWRITE BITN_ALT-BVECP-1))
 (12 2 (:REWRITE CAT_ALT-BVECP))
 (8 8 (:TYPE-PRESCRIPTION CAT_ALT-NONNEGATIVE-INTEGER-TYPE))
 (8 8 (:DEFINITION CHI_ALT))
 (4 4 (:REWRITE BITN_ALT-NEG))
 (2 2 (:REWRITE ZP-OPEN))
 )
(GAMMA)
(GAMMA-IS-GAMMA_ALT
 (18 6 (:REWRITE BVECP-BITN_ALT-0))
 (16 16 (:TYPE-PRESCRIPTION BVECP))
 (6 6 (:REWRITE NEG-BITN_ALT-2))
 (6 6 (:REWRITE NEG-BITN_ALT-1))
 (6 6 (:REWRITE NEG-BITN_ALT-0))
 (6 6 (:REWRITE BITN_ALT-NEG))
 (6 2 (:REWRITE BITN_ALT-BVECP-1))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE ZP-OPEN))
 )
(DELTA)
(DELTA-IS-DELTA_ALT
 (70 26 (:REWRITE BVECP-BITN_ALT-0))
 (56 56 (:TYPE-PRESCRIPTION BVECP))
 (40 40 (:REWRITE DEFAULT-+-2))
 (40 40 (:REWRITE DEFAULT-+-1))
 (38 26 (:REWRITE BITN_ALT-NEG))
 (28 28 (:REWRITE DEFAULT-*-2))
 (28 28 (:REWRITE DEFAULT-*-1))
 (26 26 (:REWRITE NEG-BITN_ALT-2))
 (26 26 (:REWRITE NEG-BITN_ALT-1))
 (26 26 (:REWRITE NEG-BITN_ALT-0))
 (18 6 (:REWRITE BITN_ALT-BVECP-1))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 )
(PSI)
(PSI-IS-PSI_ALT
 (62 24 (:REWRITE DEFAULT-+-2))
 (40 24 (:REWRITE DEFAULT-+-1))
 (32 32 (:TYPE-PRESCRIPTION DELTA_ALT))
 (24 24 (:TYPE-PRESCRIPTION GAMMA_ALT))
 (22 14 (:REWRITE DEFAULT-*-2))
 (14 14 (:REWRITE DEFAULT-*-1))
 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (8 4 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (6 6 (:TYPE-PRESCRIPTION BITS_ALT-NONNEGATIVE-INTEGERP-TYPE))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE BITS_ALT-NEG))
 )
(PSI-M-1)
(SUM-PSI)
(SUM-PSI-IS-SUM-PSI
 (168 6 (:DEFINITION EXPT))
 (92 70 (:REWRITE DEFAULT-+-2))
 (92 70 (:REWRITE DEFAULT-+-1))
 (60 30 (:REWRITE DEFAULT-*-2))
 (42 30 (:REWRITE DEFAULT-*-1))
 (36 12 (:REWRITE FOLD-CONSTS-IN-+))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (18 18 (:TYPE-PRESCRIPTION PSI_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE ZIP-OPEN))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 )
(SUM-PSI-LEMMA)
(PSI-BND)
(PP4-PSI
 (2 2 (:TYPE-PRESCRIPTION BMUX4))
 )
(PP4-PSI-IS-PP4_ALT-PSI_ALT
 (896 8 (:REWRITE NEG-BITN_ALT-2))
 (288 24 (:DEFINITION EXPT))
 (249 197 (:REWRITE DEFAULT-+-2))
 (224 224 (:TYPE-PRESCRIPTION LOGNOT))
 (200 200 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (200 200 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (197 197 (:REWRITE DEFAULT-+-1))
 (140 88 (:REWRITE DEFAULT-<-1))
 (136 88 (:REWRITE DEFAULT-<-2))
 (118 65 (:REWRITE DEFAULT-*-2))
 (88 8 (:REWRITE NEG-BITN_ALT-0))
 (72 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (72 24 (:REWRITE COMMUTATIVITY-OF-+))
 (72 8 (:REWRITE NEG-BITN_ALT-1))
 (65 65 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE BVECP-BITN_ALT-0))
 (24 8 (:REWRITE BITN_ALT-BVECP-1))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE BITN_ALT-NEG))
 )
(SUM-PP4-PSI)
(SUM-PP4-PSI-IS-SUM-PP4-PSI
 (22 16 (:REWRITE DEFAULT-+-2))
 (22 16 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION PP4_ALT-PSI_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 )
(REDUNDANT-BOOTH
 (20736 2 (:DEFINITION SUM-PP4_ALT-PSI_ALT))
 (20704 2 (:DEFINITION PP4_ALT-PSI_ALT))
 (17890 10 (:DEFINITION PSI_ALT))
 (12152 20 (:DEFINITION DELTA_ALT))
 (10476 216 (:REWRITE NEG-BITN_ALT-2))
 (9384 52 (:DEFINITION GAMMA_ALT))
 (3880 1806 (:REWRITE DEFAULT-+-2))
 (3036 820 (:TYPE-PRESCRIPTION LOGIOR-NATP))
 (2801 2465 (:REWRITE DEFAULT-<-2))
 (2724 768 (:TYPE-PRESCRIPTION LOGAND-NATP-2))
 (2665 2465 (:REWRITE DEFAULT-<-1))
 (2184 216 (:REWRITE NEG-BITN_ALT-0))
 (2134 1806 (:REWRITE DEFAULT-+-1))
 (1640 1640 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (1602 742 (:REWRITE DEFAULT-*-2))
 (1232 4 (:DEFINITION BMUX4_ALT))
 (1164 448 (:REWRITE FOLD-CONSTS-IN-+))
 (742 742 (:REWRITE DEFAULT-*-1))
 (568 216 (:REWRITE BVECP-BITN_ALT-0))
 (516 6 (:DEFINITION NEG))
 (480 160 (:REWRITE DEFAULT-UNARY-MINUS))
 (382 382 (:TYPE-PRESCRIPTION LOGNOT))
 (320 16 (:REWRITE BITS_ALT-TAIL-2))
 (260 164 (:REWRITE BITN_ALT-NEG))
 (248 216 (:REWRITE NEG-BITN_ALT-1))
 (194 194 (:TYPE-PRESCRIPTION BITS_ALT-NONNEGATIVE-INTEGERP-TYPE))
 (104 16 (:REWRITE BITS_ALT-TAIL))
 (98 98 (:REWRITE ZIP-OPEN))
 (81 21 (:REWRITE ZP-OPEN))
 (80 56 (:REWRITE BITN_ALT-BVECP-1))
 (56 56 (:TYPE-PRESCRIPTION NATP))
 (52 20 (:REWRITE UNICITY-OF-0))
 (40 28 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (32 28 (:REWRITE BITS_ALT-NEG))
 (32 20 (:DEFINITION FIX))
 (20 20 (:REWRITE LOGAND-COMMUTATIVE))
 (16 2 (:REWRITE CAT_ALT-0))
 (12 12 (:REWRITE LOGAND-0-Y))
 (12 2 (:REWRITE CAT_ALT-BVECP))
 (8 8 (:TYPE-PRESCRIPTION CAT_ALT-NONNEGATIVE-INTEGER-TYPE))
 (8 4 (:REWRITE LOGIOR-COMMUTATIVE-2))
 (4 4 (:REWRITE LOGIOR-COMMUTATIVE))
 )
(ETA)
(ETA-IS-ETA_ALT
 (38 16 (:REWRITE DEFAULT-+-2))
 (36 36 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (26 16 (:REWRITE DEFAULT-+-1))
 (24 8 (:REWRITE BVECP-BITN_ALT-0))
 (24 8 (:REWRITE BITN_ALT-NEG))
 (18 12 (:REWRITE DEFAULT-*-2))
 (16 16 (:TYPE-PRESCRIPTION BVECP))
 (12 12 (:REWRITE DEFAULT-*-1))
 (8 8 (:REWRITE NEG-BITN_ALT-2))
 (8 8 (:REWRITE NEG-BITN_ALT-1))
 (8 8 (:REWRITE NEG-BITN_ALT-0))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(SUM-ETA)
(SUM-ETA-IS-SUM-ETA_ALT
 (428 178 (:REWRITE DEFAULT-+-2))
 (338 178 (:REWRITE DEFAULT-+-1))
 (288 288 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (240 126 (:REWRITE DEFAULT-*-2))
 (210 126 (:REWRITE DEFAULT-*-1))
 (168 6 (:DEFINITION EXPT))
 (156 156 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (156 156 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (72 24 (:REWRITE BVECP-BITN_ALT-0))
 (60 24 (:REWRITE BITN_ALT-NEG))
 (48 48 (:TYPE-PRESCRIPTION BVECP))
 (24 24 (:REWRITE NEG-BITN_ALT-2))
 (24 24 (:REWRITE NEG-BITN_ALT-1))
 (24 24 (:REWRITE NEG-BITN_ALT-0))
 (24 24 (:REWRITE DEFAULT-<-2))
 (24 24 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE ZIP-OPEN))
 )
(SUM-ETA-LEMMA)
(BMUX8)
(BMUX8-IS-BMUX8_ALT
 (272 8 (:REWRITE BITS_ALT-TAIL-2))
 (128 8 (:DEFINITION EXPT))
 (80 8 (:REWRITE BITS_ALT-TAIL))
 (64 16 (:REWRITE FOLD-CONSTS-IN-+))
 (48 48 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (48 48 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (48 48 (:REWRITE DEFAULT-+-2))
 (48 48 (:REWRITE DEFAULT-+-1))
 (48 8 (:REWRITE COMMUTATIVITY-OF-+))
 (40 40 (:TYPE-PRESCRIPTION LOGNOT))
 (36 20 (:REWRITE DEFAULT-*-2))
 (34 18 (:REWRITE DEFAULT-<-2))
 (26 18 (:REWRITE DEFAULT-<-1))
 (20 20 (:REWRITE DEFAULT-*-1))
 (16 16 (:TYPE-PRESCRIPTION BVECP))
 (16 8 (:REWRITE UNICITY-OF-0))
 (8 8 (:REWRITE ZIP-OPEN))
 (8 8 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (8 8 (:REWRITE BITS_ALT-NEG))
 (8 8 (:DEFINITION FIX))
 )
(PP8
 (2 2 (:TYPE-PRESCRIPTION BMUX8))
 )
(PP8-IS-PP8_ALT
 (908 8 (:REWRITE NEG-BITN_ALT-2))
 (288 24 (:DEFINITION EXPT))
 (249 197 (:REWRITE DEFAULT-+-2))
 (212 212 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (212 212 (:TYPE-PRESCRIPTION LOGNOT))
 (212 212 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (197 197 (:REWRITE DEFAULT-+-1))
 (140 88 (:REWRITE DEFAULT-<-1))
 (136 88 (:REWRITE DEFAULT-<-2))
 (118 65 (:REWRITE DEFAULT-*-2))
 (88 8 (:REWRITE NEG-BITN_ALT-0))
 (72 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (72 24 (:REWRITE COMMUTATIVITY-OF-+))
 (72 8 (:REWRITE NEG-BITN_ALT-1))
 (65 65 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE BVECP-BITN_ALT-0))
 (24 8 (:REWRITE BITN_ALT-BVECP-1))
 (21 21 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE BITN_ALT-NEG))
 )
(SUM-PP8)
(SUM-PP8-SUM-PP8_ALT
 (22 16 (:REWRITE DEFAULT-+-2))
 (22 16 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION PP8_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 )
(BOOTH8-THM
 (520 23 (:DEFINITION EXPT))
 (366 228 (:REWRITE DEFAULT-+-2))
 (316 228 (:REWRITE DEFAULT-+-1))
 (234 103 (:REWRITE DEFAULT-*-2))
 (150 66 (:REWRITE FOLD-CONSTS-IN-+))
 (133 103 (:REWRITE DEFAULT-*-1))
 (34 31 (:REWRITE DEFAULT-<-1))
 (31 31 (:REWRITE DEFAULT-<-2))
 (20 8 (:REWRITE ZP-OPEN))
 (17 17 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (15 15 (:REWRITE ZIP-OPEN))
 (12 4 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(PP8-ETA
 (2 2 (:TYPE-PRESCRIPTION BMUX8))
 )
(PP8-ETA-IS-PP8-ETA_ALT
 (1088 32 (:REWRITE BITS_ALT-TAIL-2))
 (976 88 (:REWRITE NEG-BITN_ALT-2))
 (825 553 (:REWRITE DEFAULT-+-2))
 (800 56 (:DEFINITION EXPT))
 (653 553 (:REWRITE DEFAULT-+-1))
 (418 249 (:REWRITE DEFAULT-*-2))
 (392 392 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (392 392 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (384 384 (:TYPE-PRESCRIPTION LOGNOT))
 (320 200 (:REWRITE DEFAULT-<-1))
 (320 32 (:REWRITE BITS_ALT-TAIL))
 (312 200 (:REWRITE DEFAULT-<-2))
 (264 88 (:REWRITE BVECP-BITN_ALT-0))
 (264 56 (:REWRITE COMMUTATIVITY-OF-+))
 (249 249 (:REWRITE DEFAULT-*-1))
 (184 88 (:REWRITE BITN_ALT-NEG))
 (168 88 (:REWRITE NEG-BITN_ALT-0))
 (152 88 (:REWRITE NEG-BITN_ALT-1))
 (72 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (48 16 (:REWRITE BITN_ALT-BVECP-1))
 (32 32 (:REWRITE ZIP-OPEN))
 (32 32 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (32 32 (:REWRITE BITS_ALT-NEG))
 (21 21 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(SUM-PP8-ETA)
(SUM-PP8-ETA-IS-SUM-PP8_ALT-ETA_ALT
 (22 16 (:REWRITE DEFAULT-+-2))
 (22 16 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION PP8_ALT-ETA_ALT))
 (6 6 (:REWRITE ZP-OPEN))
 )
(BOOTH8-COROLLARY
 (3932 2 (:DEFINITION SUM-PP8_ALT-ETA_ALT))
 (3900 2 (:DEFINITION PP8_ALT-ETA_ALT))
 (2478 10 (:DEFINITION ETA_ALT))
 (1154 42 (:REWRITE NEG-BITN_ALT-2))
 (1058 60 (:DEFINITION EXPT))
 (904 4 (:DEFINITION BMUX8_ALT))
 (642 42 (:REWRITE NEG-BITN_ALT-0))
 (586 464 (:REWRITE DEFAULT-+-2))
 (560 8 (:REWRITE BITS_ALT-TAIL-2))
 (516 464 (:REWRITE DEFAULT-+-1))
 (406 330 (:REWRITE DEFAULT-<-2))
 (390 390 (:TYPE-PRESCRIPTION BITN_ALT-NONNEGATIVE-INTEGER))
 (366 330 (:REWRITE DEFAULT-<-1))
 (352 136 (:REWRITE FOLD-CONSTS-IN-+))
 (346 182 (:REWRITE DEFAULT-*-2))
 (182 182 (:REWRITE DEFAULT-*-1))
 (170 34 (:REWRITE DISTRIBUTIVITY))
 (118 42 (:REWRITE BVECP-BITN_ALT-0))
 (96 10 (:REWRITE COMMUTATIVITY-2-OF-+))
 (90 30 (:REWRITE DEFAULT-UNARY-MINUS))
 (86 86 (:TYPE-PRESCRIPTION LOGNOT))
 (80 8 (:REWRITE BITS_ALT-TAIL))
 (78 38 (:REWRITE BITN_ALT-NEG))
 (72 6 (:DEFINITION NEG))
 (58 42 (:REWRITE NEG-BITN_ALT-1))
 (48 16 (:REWRITE UNICITY-OF-0))
 (44 20 (:DEFINITION NATP))
 (36 36 (:REWRITE ZIP-OPEN))
 (32 16 (:DEFINITION FIX))
 (20 20 (:TYPE-PRESCRIPTION NATP))
 (18 6 (:REWRITE BITN_ALT-BVECP-1))
 (16 2 (:REWRITE CAT_ALT-0))
 (12 2 (:REWRITE CAT_ALT-BVECP))
 (8 8 (:TYPE-PRESCRIPTION CAT_ALT-NONNEGATIVE-INTEGER-TYPE))
 (8 8 (:REWRITE BITS_ALT-WITH-INDICES-IN-THE-WRONG-ORDER))
 (8 8 (:REWRITE BITS_ALT-NEG))
 (2 2 (:REWRITE ZP-OPEN))
 )
