(ZCASH::BIT-LISTP-OF-TAKE-3
 (292 292 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (292 292 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (89 12 (:REWRITE BIT-LISTP-WHEN-NOT-CONSP))
 (38 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (36 36 (:LINEAR LOWER-BOUND-OF-LEN-WHEN-SUBLISTP))
 (36 36 (:LINEAR LISTPOS-UPPER-BOUND-STRONG-2))
 (36 36 (:LINEAR LEN-WHEN-PREFIXP))
 (32 28 (:REWRITE LEN-WHEN-ATOM))
 (32 16 (:REWRITE SIMPLIFY-SUMS-<))
 (32 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (32 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (31 16 (:REWRITE DEFAULT-<-1))
 (30 15 (:REWRITE DEFAULT-*-2))
 (29 1 (:REWRITE TAKE-OF-LEN-FREE))
 (26 1 (:REWRITE TAKE-OF-TOO-MANY))
 (22 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (18 18 (:LINEAR INDEX-OF-<-LEN))
 (17 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:REWRITE DEFAULT-*-1))
 (15 15 (:REWRITE |(integerp (* c x))|))
 (15 15 (:META META-INTEGERP-CORRECT))
 (11 11 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (11 11 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (11 11 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (11 11 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (11 11 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (11 11 (:REWRITE CONSP-BY-LEN))
 (8 8 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:TYPE-PRESCRIPTION NFIX))
 (1 1 (:REWRITE TAKE-WHEN-ATOM))
 (1 1 (:REWRITE SUBSETP-TRANS2))
 (1 1 (:REWRITE SUBSETP-TRANS))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(ZCASH::LEN-OF-NTHCDR-MULTIPLE-OF-3
 (25 5 (:DEFINITION LEN))
 (18 10 (:REWRITE DEFAULT-+-2))
 (11 10 (:REWRITE DEFAULT-+-1))
 (10 5 (:REWRITE DEFAULT-*-2))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-*-1))
 (4 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (2 2 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (2 2 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (2 2 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 )
(ZCASH::INDUCTION
 (3748 17 (:DEFINITION ACL2-COUNT))
 (1351 65 (:REWRITE INTEGERP-OF-CAR-WHEN-INTEGER-LISTP))
 (1299 35 (:DEFINITION INTEGER-LISTP))
 (1231 65 (:REWRITE RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP))
 (1179 35 (:DEFINITION RATIONAL-LISTP))
 (826 73 (:REWRITE INTEGER-LISTP-OF-CDR-WHEN-INTEGER-LISTP))
 (756 73 (:REWRITE RATIONAL-LISTP-OF-CDR-WHEN-RATIONAL-LISTP))
 (573 391 (:REWRITE DEFAULT-CDR))
 (345 123 (:REWRITE DEFAULT-+-2))
 (336 92 (:REWRITE RATIONAL-LISTP-WHEN-NOT-CONSP))
 (336 92 (:REWRITE INTEGER-LISTP-WHEN-NOT-CONSP))
 (322 14 (:DEFINITION LENGTH))
 (292 292 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (292 292 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (292 292 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (292 292 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (280 14 (:DEFINITION LEN))
 (223 123 (:REWRITE DEFAULT-+-1))
 (155 143 (:REWRITE DEFAULT-CAR))
 (140 28 (:REWRITE COMMUTATIVITY-OF-+))
 (130 65 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (112 28 (:DEFINITION INTEGER-ABS))
 (65 65 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (56 28 (:REWRITE STR::CONSP-OF-EXPLODE))
 (42 42 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (31 31 (:REWRITE FOLD-CONSTS-IN-+))
 (31 29 (:REWRITE DEFAULT-<-2))
 (31 29 (:REWRITE DEFAULT-<-1))
 (28 28 (:REWRITE DEFAULT-UNARY-MINUS))
 (28 14 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (20 4 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (16 8 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (15 15 (:REWRITE EQUAL-CONSTANT-WHEN-BVCHOP-EQUAL-CONSTANT-FALSE))
 (15 3 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (14 14 (:TYPE-PRESCRIPTION LEN))
 (14 14 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (14 14 (:REWRITE DEFAULT-REALPART))
 (14 14 (:REWRITE DEFAULT-NUMERATOR))
 (14 14 (:REWRITE DEFAULT-IMAGPART))
 (14 14 (:REWRITE DEFAULT-DENOMINATOR))
 (14 1 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (9 1 (:DEFINITION MEMBER-EQUAL))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (8 8 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (5 5 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:REWRITE SUBSETP-MEMBER . 2))
 (2 2 (:REWRITE SUBSETP-MEMBER . 1))
 )
(ZCASH::PRED)
(ZCASH::BASE-CASE-1
 (714 17 (:DEFINITION TAKE))
 (544 34 (:REWRITE TAKE-OF-TOO-MANY))
 (536 80 (:DEFINITION LEN))
 (476 34 (:REWRITE TAKE-OF-LEN-FREE))
 (469 144 (:REWRITE DEFAULT-*-2))
 (398 216 (:REWRITE DEFAULT-+-2))
 (384 24 (:DEFINITION EXPT))
 (335 199 (:REWRITE DEFAULT-CDR))
 (318 216 (:REWRITE DEFAULT-+-1))
 (191 144 (:REWRITE DEFAULT-*-1))
 (107 63 (:REWRITE DEFAULT-<-2))
 (102 34 (:REWRITE TAKE-WHEN-ATOM))
 (96 24 (:REWRITE 0-<-*))
 (94 94 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (94 94 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (94 94 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (94 94 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (70 63 (:REWRITE DEFAULT-<-1))
 (68 68 (:TYPE-PRESCRIPTION ZCASH::PEDERSEN-ENC-NOT-ZERO))
 (68 68 (:TYPE-PRESCRIPTION ZCASH::INTEGERP-OF-PEDERSEN-ENC))
 (34 34 (:TYPE-PRESCRIPTION NFIX))
 (34 34 (:REWRITE FOLD-CONSTS-IN-*))
 (24 24 (:DEFINITION IFF))
 (24 9 (:REWRITE DEFAULT-UNARY-MINUS))
 (18 3 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (17 17 (:REWRITE DEFAULT-CAR))
 (15 3 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (15 3 (:REWRITE BIT-LISTP-WHEN-NOT-CONSP))
 (12 3 (:REWRITE NATP-POSP))
 (6 6 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:REWRITE POSP-WHEN-MEMBER-EQUAL-OF-ZP-LISTP))
 (6 3 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (4 4 (:REWRITE SUBSETP-TRANS2))
 (4 4 (:REWRITE SUBSETP-TRANS))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (3 3 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-UNSIGNED-BYTE-LISTP))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-SIGNED-BYTE-LISTP))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-DAB-DIGIT-LISTP))
 (3 3 (:REWRITE POSP-RW))
 (3 3 (:REWRITE NATP-RW))
 (3 3 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE EQUAL-CONSTANT-WHEN-BVCHOP-EQUAL-CONSTANT-FALSE))
 )
(ZCASH::BASE-CASE-2
 (210 5 (:DEFINITION TAKE))
 (160 24 (:DEFINITION LEN))
 (160 10 (:REWRITE TAKE-OF-TOO-MANY))
 (155 49 (:REWRITE DEFAULT-*-2))
 (140 10 (:REWRITE TAKE-OF-LEN-FREE))
 (128 8 (:DEFINITION EXPT))
 (122 68 (:REWRITE DEFAULT-+-2))
 (105 20 (:REWRITE OPEN-SMALL-NTHCDR))
 (99 59 (:REWRITE DEFAULT-CDR))
 (98 68 (:REWRITE DEFAULT-+-1))
 (95 15 (:REWRITE NTHCDR-OF-CDR))
 (80 5 (:REWRITE COMMUTATIVITY-2-OF-*))
 (69 13 (:REWRITE COMMUTATIVITY-OF-+))
 (64 49 (:REWRITE DEFAULT-*-1))
 (37 37 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (37 37 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (37 37 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (37 37 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (35 21 (:REWRITE DEFAULT-<-2))
 (32 8 (:REWRITE 0-<-*))
 (30 10 (:REWRITE TAKE-WHEN-ATOM))
 (28 21 (:REWRITE DEFAULT-<-1))
 (25 5 (:REWRITE DISTRIBUTIVITY))
 (20 20 (:TYPE-PRESCRIPTION ZCASH::PEDERSEN-ENC-NOT-ZERO))
 (20 20 (:TYPE-PRESCRIPTION ZCASH::INTEGERP-OF-PEDERSEN-ENC))
 (18 3 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (15 3 (:REWRITE BIT-LISTP-WHEN-NOT-CONSP))
 (15 3 (:DEFINITION ATOM))
 (12 3 (:REWRITE NATP-POSP))
 (10 10 (:TYPE-PRESCRIPTION NFIX))
 (10 10 (:REWRITE FOLD-CONSTS-IN-*))
 (8 8 (:REWRITE SUBSETP-TRANS2))
 (8 8 (:REWRITE SUBSETP-TRANS))
 (8 8 (:DEFINITION IFF))
 (8 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 6 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:REWRITE POSP-WHEN-MEMBER-EQUAL-OF-ZP-LISTP))
 (6 3 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-UNSIGNED-BYTE-LISTP))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-SIGNED-BYTE-LISTP))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-DAB-DIGIT-LISTP))
 (3 3 (:REWRITE POSP-RW))
 (3 3 (:REWRITE NATP-RW))
 (3 3 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE EQUAL-CONSTANT-WHEN-BVCHOP-EQUAL-CONSTANT-FALSE))
 (1 1 (:LINEAR ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-UPPER-BOUND))
 (1 1 (:LINEAR ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-LOWER-BOUND))
 )
(ZCASH::FIRST-DIFFERENCE
 (29745 661 (:DEFINITION EXPT))
 (15529 4343 (:REWRITE DEFAULT-+-2))
 (11769 2768 (:REWRITE DEFAULT-*-2))
 (9327 4343 (:REWRITE DEFAULT-+-1))
 (5949 661 (:REWRITE ZIP-OPEN))
 (5558 2768 (:REWRITE DEFAULT-*-1))
 (3390 678 (:REWRITE DEFAULT-CAR))
 (3330 698 (:REWRITE DEFAULT-CDR))
 (3082 833 (:REWRITE DEFAULT-<-2))
 (2768 692 (:REWRITE <-0-+-NEGATIVE-1))
 (2226 352 (:REWRITE DEFAULT-UNARY-MINUS))
 (2127 2127 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2111 833 (:REWRITE DEFAULT-<-1))
 (1983 661 (:REWRITE EQUAL-CONSTANT-+))
 (1396 1396 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (1396 1396 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (1396 1396 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (1396 1396 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (1339 1339 (:REWRITE EQUAL-CONSTANT-WHEN-BVCHOP-EQUAL-CONSTANT-FALSE))
 (1193 33 (:LINEAR X*Y>1-POSITIVE))
 (1004 44 (:REWRITE BFIX-BITP))
 (784 44 (:REWRITE BITP-OF-CAR-WHEN-BIT-LISTP))
 (661 661 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (661 661 (:REWRITE EXPONENTS-ADD))
 (424 60 (:REWRITE BIT-LISTP-OF-CDR-WHEN-BIT-LISTP))
 (324 84 (:REWRITE BIT-LISTP-WHEN-NOT-CONSP))
 (217 31 (:LINEAR EXPT->-1))
 (168 168 (:REWRITE BIT-LISTP-WHEN-SUBSETP-EQUAL))
 (88 88 (:REWRITE BITP-WHEN-MEMBER-EQUAL-OF-BIT-LISTP))
 (62 62 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (44 44 (:TYPE-PRESCRIPTION BITP))
 (44 44 (:DEFINITION BITP))
 (8 8 (:REWRITE-QUOTED-CONSTANT FIX-UNDER-NUMBER-EQUIV))
 (5 5 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (5 5 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 )
(ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-IS-MULTIPLE-OF-16^J-1
 (531 64 (:REWRITE DEFAULT-TIMES-2))
 (352 8 (:REWRITE TAKE-OF-TOO-MANY))
 (344 4 (:DEFINITION TAKE))
 (276 64 (:REWRITE DEFAULT-TIMES-1))
 (240 8 (:REWRITE TAKE-OF-LEN-FREE))
 (200 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (180 180 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (180 180 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (180 180 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (180 180 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (144 16 (:DEFINITION LEN))
 (137 42 (:REWRITE DEFAULT-PLUS-2))
 (136 136 (:TYPE-PRESCRIPTION LEN))
 (117 42 (:REWRITE DEFAULT-PLUS-1))
 (83 83 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A-EXPT))
 (83 83 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A-EXPT))
 (83 83 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A-EXPT))
 (77 73 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D-EXPT))
 (77 73 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D-EXPT))
 (77 73 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D-EXPT))
 (68 34 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (63 12 (:REWRITE OPEN-SMALL-NTHCDR))
 (62 38 (:REWRITE DEFAULT-CDR))
 (57 9 (:REWRITE NTHCDR-OF-CDR))
 (39 9 (:META META-INTEGERP-CORRECT))
 (35 35 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (34 34 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (24 8 (:REWRITE TAKE-WHEN-ATOM))
 (23 23 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (23 23 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (23 23 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (23 23 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (22 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B-EXPT))
 (22 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B-EXPT))
 (21 13 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (21 13 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (21 13 (:REWRITE DEFAULT-LESS-THAN-2))
 (21 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (20 20 (:REWRITE DEFAULT-EXPT-2))
 (20 20 (:REWRITE DEFAULT-EXPT-1))
 (16 8 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (16 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (13 13 (:REWRITE THE-FLOOR-BELOW))
 (13 13 (:REWRITE THE-FLOOR-ABOVE))
 (13 13 (:REWRITE SIMPLIFY-SUMS-<))
 (13 13 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (13 13 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13 13 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (13 13 (:REWRITE INTEGERP-<-CONSTANT))
 (13 13 (:REWRITE DEFAULT-LESS-THAN-1))
 (13 13 (:REWRITE CONSTANT-<-INTEGERP))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (- x))|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) (/ y))|))
 (13 13 (:REWRITE |(< (- x) c)|))
 (13 13 (:REWRITE |(< (- x) (- y))|))
 (10 10 (:REWRITE |(* c (* d x))|))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:TYPE-PRESCRIPTION NFIX))
 (8 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (8 8 (:REWRITE |(equal (- x) c)|))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (8 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B-EXPT))
 (7 7 (:REWRITE DEFAULT-MINUS))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (5 5 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< 0 (/ x))|))
 (5 5 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B-EXPT))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4F-EXPT-B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3F-EXPT-B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2F-EXPT-B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1F-EXPT-B))
 (1 1 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(ZCASH::DIFFERENCE-OF-MULTIPLES-IS-MULTIPLE
 (234 26 (:REWRITE ACL2-NUMBERP-X))
 (104 26 (:REWRITE RATIONALP-X))
 (61 61 (:REWRITE DEFAULT-TIMES-2))
 (59 59 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (59 59 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (59 59 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-INTEGERP-CORRECT))
 (26 26 (:REWRITE REDUCE-RATIONALP-+))
 (26 26 (:REWRITE REDUCE-RATIONALP-*))
 (26 26 (:REWRITE RATIONALP-MINUS-X))
 (26 26 (:META META-RATIONALP-CORRECT))
 (15 15 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (15 15 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (15 15 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (15 15 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (10 10 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (3 3 (:REWRITE |(- (* c x))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 )
(ZCASH::SECOND-DIFFERENCE
 (212 106 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (174 66 (:REWRITE DEFAULT-CDR))
 (108 9 (:DEFINITION EXPT))
 (106 106 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (82 31 (:REWRITE DEFAULT-*-2))
 (70 57 (:REWRITE DEFAULT-+-2))
 (70 57 (:REWRITE DEFAULT-+-1))
 (68 31 (:REWRITE DEFAULT-*-1))
 (45 9 (:REWRITE DEFAULT-UNARY-/))
 (27 27 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (27 27 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (27 27 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (27 27 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(ZCASH::LEMMA1
 (6 4 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (4 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 1 (:REWRITE NATP-POSP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE POSP-WHEN-MEMBER-EQUAL-OF-ZP-LISTP))
 (2 2 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (2 2 (:REWRITE DEFAULT-UNARY-/))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE FOLD-CONSTS-IN-*))
 )
(ZCASH::LEMMA2
 (34 22 (:REWRITE DEFAULT-TIMES-2))
 (22 22 (:REWRITE DEFAULT-TIMES-1))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (7 7 (:REWRITE INTEGERP-<-CONSTANT))
 (7 7 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (- x))|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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(ZCASH::STEP-CASE-LEMMA)
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(ZCASH::PRED-HOLDS
 (56 24 (:REWRITE DEFAULT-CDR))
 (19 19 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (19 19 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (19 19 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (19 19 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (4 2 (:REWRITE DEFAULT-+-2))
 (3 3 (:TYPE-PRESCRIPTION ZCASH::INDUCTION))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-INJECTIVITY
 (45 5 (:DEFINITION LEN))
 (25 5 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (25 5 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (24 24 (:TYPE-PRESCRIPTION POSP))
 (21 21 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 2))
 (21 21 (:REWRITE CONSP-WHEN-MEMBER-EQUAL-OF-SYMBOL-SYMBOL-ALISTP . 1))
 (21 21 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 2))
 (21 21 (:REWRITE ISAR::CONSP-WHEN-MEMBER-EQUAL-OF-KEYWORD-FACT-INFO-ALISTP . 1))
 (20 4 (:REWRITE BIT-LISTP-WHEN-NOT-CONSP))
 (15 10 (:REWRITE DEFAULT-*-2))
 (15 10 (:REWRITE DEFAULT-*-1))
 (10 5 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE SUBSETP-TRANS2))
 (7 7 (:REWRITE SUBSETP-TRANS))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 1 (:LINEAR ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-UPPER-BOUND))
 (5 1 (:LINEAR ZCASH::PEDERSEN-SEGMENT-SCALAR-LOOP-LOWER-BOUND))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(ZCASH::PEDERSEN-SEGMENT-SCALAR-INJECTIVITY
 (20 10 (:TYPE-PRESCRIPTION ZCASH::PEDERSEN-SEGMENT-SCALAR-NOT-ZERO))
 )
