(HACK516
 (570 570 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (570 570 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (570 570 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (542 542 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (393 37 (:REWRITE DEFAULT-*-2))
 (198 198 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (188 11 (:REWRITE DEFAULT-UNARY-/))
 (139 37 (:REWRITE DEFAULT-*-1))
 (58 38 (:REWRITE DEFAULT-<-2))
 (54 54 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (45 38 (:REWRITE DEFAULT-<-1))
 (36 36 (:REWRITE DEFAULT-+-2))
 (36 36 (:REWRITE DEFAULT-+-1))
 (24 7 (:REWRITE <-0-MINUS))
 (22 10 (:REWRITE ZIP-OPEN))
 (16 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 4 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE>1))
 (16 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (16 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (16 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (8 8 (:REWRITE FOLD-CONSTS-IN-*))
 (8 2 (:LINEAR EXPT->-1-2))
 (8 2 (:LINEAR EXPT->-1-1))
 (8 2 (:LINEAR EXPT-<-1-2))
 (8 2 (:LINEAR EXPT-<-1-1))
 )
(COLLECT-+)
(COLLECT-+-PROBLEM-FINDER)
(|(+ x x)|)
(|(+ x (- x))|)
(|(+ x (* c x))|
 (9 7 (:REWRITE DEFAULT-*-2))
 (9 7 (:REWRITE DEFAULT-*-1))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 5 (:REWRITE DEFAULT-+-1))
 (6 5 (:REWRITE DEFAULT-+-2))
 )
(|(+ (- x) (* c x))|
 (9 7 (:REWRITE DEFAULT-*-2))
 (9 7 (:REWRITE DEFAULT-*-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE FUNCTIONAL-COMMUTATIVITY-OF-MINUS-*-RIGHT))
 (1 1 (:REWRITE FUNCTIONAL-COMMUTATIVITY-OF-MINUS-*-LEFT))
 )
(|(+ (* c x) (* d x))|
 (11 8 (:REWRITE DEFAULT-*-2))
 (11 8 (:REWRITE DEFAULT-*-1))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 3 (:REWRITE DEFAULT-+-2))
 (4 3 (:REWRITE DEFAULT-+-1))
 )
(|(collect-+ y x)|)
(POW-2)
(COLLECT-*)
(COLLECT-*-PROBLEM-FINDER)
(|(* x x)|
 (22 22 (:TYPE-PRESCRIPTION NONNEGATIVE-PRODUCT))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT-A))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
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 (3 2 (:REWRITE DEFAULT-*-2))
 )
(|(* x (/ x))|
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 2 (:REWRITE DEFAULT-UNARY-/))
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 (2 2 (:REWRITE DEFAULT-*-2))
 )
(|(* x (expt x n))|
 (242 6 (:DEFINITION EXPT))
 (190 22 (:REWRITE DEFAULT-*-2))
 (137 137 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (137 137 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (137 137 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (137 137 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (137 137 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (137 137 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (67 67 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (53 22 (:REWRITE DEFAULT-*-1))
 (27 27 (:REWRITE DEFAULT-+-2))
 (27 27 (:REWRITE DEFAULT-+-1))
 (14 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (13 7 (:REWRITE DEFAULT-UNARY-/))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE ZIP-OPEN))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* c (expt d n))|
 (202 6 (:DEFINITION EXPT))
 (134 134 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (134 134 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (106 16 (:REWRITE DEFAULT-*-2))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (30 16 (:REWRITE DEFAULT-*-1))
 (25 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
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 (12 6 (:REWRITE ZIP-OPEN))
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 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
 (2 2 (:REWRITE |(expt x (* c n))|))
 )
(|(* (- c) (expt c n))|
 (191 23 (:REWRITE DEFAULT-*-2))
 (70 70 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (70 70 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (70 70 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (70 70 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (70 70 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (70 70 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (52 52 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (27 27 (:REWRITE DEFAULT-+-2))
 (27 27 (:REWRITE DEFAULT-+-1))
 (26 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (13 7 (:REWRITE DEFAULT-UNARY-/))
 (7 7 (:REWRITE ZIP-OPEN))
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 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* (- c) (expt d n))|
 (202 6 (:DEFINITION EXPT))
 (139 139 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (139 139 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (106 16 (:REWRITE DEFAULT-*-2))
 (38 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (30 16 (:REWRITE DEFAULT-*-1))
 (25 25 (:REWRITE DEFAULT-+-2))
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 (16 2 (:REWRITE 0-<-*))
 (12 6 (:REWRITE ZIP-OPEN))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
 (2 2 (:REWRITE |(expt x (* c n))|))
 )
(|(* (/ x) (expt x n))|
 (166 4 (:DEFINITION EXPT))
 (130 16 (:REWRITE DEFAULT-*-2))
 (94 94 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (94 94 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (94 94 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (94 94 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (94 94 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (94 94 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (59 59 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (37 16 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (18 18 (:REWRITE DEFAULT-+-2))
 (18 18 (:REWRITE DEFAULT-+-1))
 (18 9 (:REWRITE DEFAULT-UNARY-/))
 (14 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE ZIP-OPEN))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(|(* (/ c) (expt d n))|
 (202 6 (:DEFINITION EXPT))
 (138 138 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (138 138 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (106 16 (:REWRITE DEFAULT-*-2))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (30 16 (:REWRITE DEFAULT-*-1))
 (30 2 (:REWRITE DEFAULT-UNARY-/))
 (25 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (16 2 (:REWRITE 0-<-*))
 (12 6 (:REWRITE ZIP-OPEN))
 (10 10 (:REWRITE DEFAULT-<-2))
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 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
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 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(|(* (- (/ c)) (expt c n))|
 (130 16 (:REWRITE DEFAULT-*-2))
 (61 61 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (61 61 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (61 61 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (61 61 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (61 61 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (61 61 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (52 52 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (37 16 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (24 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (18 18 (:REWRITE DEFAULT-+-2))
 (18 18 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE ZIP-OPEN))
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 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* (- (/ c)) (expt d n))|
 (202 6 (:DEFINITION EXPT))
 (143 143 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (143 143 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (106 16 (:REWRITE DEFAULT-*-2))
 (39 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (30 16 (:REWRITE DEFAULT-*-1))
 (30 2 (:REWRITE DEFAULT-UNARY-/))
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 (12 6 (:REWRITE ZIP-OPEN))
 (10 10 (:REWRITE DEFAULT-<-2))
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 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
 (2 2 (:REWRITE |(expt x (* c n))|))
 )
(|(* x (/ (expt x n)))|
 (303 10 (:REWRITE DEFAULT-UNARY-/))
 (166 4 (:DEFINITION EXPT))
 (129 15 (:REWRITE DEFAULT-*-2))
 (119 119 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (49 29 (:REWRITE DEFAULT-<-2))
 (38 38 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (37 15 (:REWRITE DEFAULT-*-1))
 (33 29 (:REWRITE DEFAULT-<-1))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (18 18 (:REWRITE DEFAULT-+-2))
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 (16 4 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE>1))
 (16 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (16 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (16 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (8 2 (:LINEAR EXPT->-1-2))
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 (8 2 (:LINEAR EXPT-<-1-2))
 (8 2 (:LINEAR EXPT-<-1-1))
 (5 1 (:REWRITE EQUAL-EXPT-0))
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 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:DEFINITION IFIX))
 )
(|(* c (/ (expt d n)))|
 (202 6 (:DEFINITION EXPT))
 (143 143 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (143 143 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (114 17 (:REWRITE DEFAULT-*-2))
 (45 3 (:REWRITE DEFAULT-UNARY-/))
 (38 17 (:REWRITE DEFAULT-*-1))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (25 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (16 2 (:REWRITE 0-<-*))
 (12 6 (:REWRITE ZIP-OPEN))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
 (2 2 (:REWRITE |(expt x (* c n))|))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(|(* (- c) (/ (expt c n)))|
 (304 11 (:REWRITE DEFAULT-UNARY-/))
 (130 16 (:REWRITE DEFAULT-*-2))
 (80 80 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (80 80 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (80 80 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (80 80 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (80 80 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (80 80 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (67 67 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
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 (16 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (16 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (16 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (8 2 (:LINEAR EXPT->-1-2))
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 (8 2 (:LINEAR EXPT-<-1-2))
 (8 2 (:LINEAR EXPT-<-1-1))
 (5 5 (:REWRITE ZIP-OPEN))
 (5 1 (:REWRITE EQUAL-EXPT-0))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
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 (1 1 (:DEFINITION IFIX))
 )
(|(* (- c) (/ (expt d n)))|
 (202 6 (:DEFINITION EXPT))
 (148 148 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (148 148 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
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 (2 2 (:REWRITE |(expt x (* c n))|))
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(|(* (/ x) (/ (expt x n)))|
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 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
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 (16 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
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 (8 2 (:LINEAR EXPT-<-1-1))
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 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 (1 1 (:DEFINITION IFIX))
 )
(|(* (/ c) (/ (expt d n)))|
 (202 6 (:DEFINITION EXPT))
 (144 144 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (144 144 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
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 (25 25 (:REWRITE DEFAULT-+-2))
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 (6 2 (:REWRITE EQUAL-*-X-Y-0))
 (6 2 (:DEFINITION IFF))
 (2 2 (:REWRITE |(expt x (* c n))|))
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(|(* (- (/ c)) (/ (expt c n)))|
 (191 23 (:REWRITE DEFAULT-*-2))
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 (93 93 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (93 93 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (93 93 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (93 93 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
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 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
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(|(* (- (/ c)) (/ (expt d n)))|
 (202 6 (:DEFINITION EXPT))
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 (2 2 (:REWRITE |(expt x (* c n))|))
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(|(* (expt x m) (expt x n))|
 (195 195 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
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 (195 195 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
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 (147 147 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
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 )
(|(* (expt c m) (expt d n))|
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 (4 4 (:REWRITE |(expt x (* c n))|))
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(|(* (/ (expt x m)) (expt x n))|
 (381 9 (:REWRITE DEFAULT-UNARY-/))
 (201 201 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (201 201 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (201 201 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (173 173 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (170 16 (:REWRITE DEFAULT-*-2))
 (161 161 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (96 56 (:REWRITE DEFAULT-<-2))
 (69 69 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (64 56 (:REWRITE DEFAULT-<-1))
 (58 16 (:REWRITE DEFAULT-*-1))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (32 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (27 27 (:REWRITE DEFAULT-+-2))
 (27 27 (:REWRITE DEFAULT-+-1))
 (16 4 (:LINEAR EXPT->-1-2))
 (16 4 (:LINEAR EXPT->-1-1))
 (16 4 (:LINEAR EXPT-<-1-2))
 (16 4 (:LINEAR EXPT-<-1-1))
 (10 2 (:REWRITE EQUAL-EXPT-0))
 (6 6 (:REWRITE ZIP-OPEN))
 (4 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (4 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (3 1 (:REWRITE <-MINUS-ZERO))
 (3 1 (:REWRITE <-0-MINUS))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:DEFINITION IFIX))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* (/ (expt c m)) (expt d n))|
 (284 8 (:DEFINITION EXPT))
 (177 177 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (177 177 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (140 22 (:REWRITE DEFAULT-*-2))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (36 22 (:REWRITE DEFAULT-*-1))
 (33 33 (:REWRITE DEFAULT-+-2))
 (33 33 (:REWRITE DEFAULT-+-1))
 (32 4 (:REWRITE 0-<-*))
 (30 2 (:REWRITE DEFAULT-UNARY-/))
 (20 8 (:REWRITE ZIP-OPEN))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE EQUAL-*-X-Y-0))
 (12 4 (:DEFINITION IFF))
 (4 4 (:REWRITE |(expt x (* c n))|))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(|(* (expt x m) (/ (expt x n)))|
 (381 9 (:REWRITE DEFAULT-UNARY-/))
 (199 199 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (199 199 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (199 199 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (171 171 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (161 161 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (160 15 (:REWRITE DEFAULT-*-2))
 (96 56 (:REWRITE DEFAULT-<-2))
 (69 69 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (64 56 (:REWRITE DEFAULT-<-1))
 (48 15 (:REWRITE DEFAULT-*-1))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (32 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (26 26 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE DEFAULT-+-1))
 (16 4 (:LINEAR EXPT->-1-2))
 (16 4 (:LINEAR EXPT->-1-1))
 (16 4 (:LINEAR EXPT-<-1-2))
 (16 4 (:LINEAR EXPT-<-1-1))
 (10 2 (:REWRITE EQUAL-EXPT-0))
 (6 6 (:REWRITE ZIP-OPEN))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:DEFINITION IFIX))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* (expt c m) (/ (expt d n)))|
 (284 8 (:DEFINITION EXPT))
 (177 177 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (177 177 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (140 22 (:REWRITE DEFAULT-*-2))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (36 22 (:REWRITE DEFAULT-*-1))
 (33 33 (:REWRITE DEFAULT-+-2))
 (33 33 (:REWRITE DEFAULT-+-1))
 (32 4 (:REWRITE 0-<-*))
 (30 2 (:REWRITE DEFAULT-UNARY-/))
 (20 8 (:REWRITE ZIP-OPEN))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE EQUAL-*-X-Y-0))
 (12 4 (:DEFINITION IFF))
 (4 4 (:REWRITE |(expt x (* c n))|))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(|(* (/ (expt x m)) (/ (expt x n)))|
 (561 11 (:REWRITE DEFAULT-UNARY-/))
 (226 226 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (226 226 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (226 226 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (198 198 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (177 177 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (160 15 (:REWRITE DEFAULT-*-2))
 (96 56 (:REWRITE DEFAULT-<-2))
 (71 71 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (64 56 (:REWRITE DEFAULT-<-1))
 (48 15 (:REWRITE DEFAULT-*-1))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE<1))
 (32 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (32 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE<1))
 (26 26 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE DEFAULT-+-1))
 (16 4 (:LINEAR EXPT->-1-2))
 (16 4 (:LINEAR EXPT->-1-1))
 (16 4 (:LINEAR EXPT-<-1-2))
 (16 4 (:LINEAR EXPT-<-1-1))
 (10 2 (:REWRITE EQUAL-EXPT-0))
 (6 6 (:REWRITE ZIP-OPEN))
 (5 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONPOS-EXPONENTS))
 (3 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:DEFINITION IFIX))
 (1 1 (:REWRITE EXPONENTS-ADD-2))
 )
(|(* (/ (expt c m)) (/ (expt d n)))|
 (284 8 (:DEFINITION EXPT))
 (183 183 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (183 183 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (148 23 (:REWRITE DEFAULT-*-2))
 (60 4 (:REWRITE DEFAULT-UNARY-/))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (44 23 (:REWRITE DEFAULT-*-1))
 (33 33 (:REWRITE DEFAULT-+-2))
 (33 33 (:REWRITE DEFAULT-+-1))
 (32 4 (:REWRITE 0-<-*))
 (20 8 (:REWRITE ZIP-OPEN))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE EQUAL-*-X-Y-0))
 (12 4 (:DEFINITION IFF))
 (4 4 (:REWRITE |(expt x (* c n))|))
 )
(|(* (expt x n) (expt y n))|
 (180 4 (:DEFINITION EXPT))
 (112 11 (:REWRITE DEFAULT-*-2))
 (75 75 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-2))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-1))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-ZERO-BASE))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT-A))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (36 11 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (18 18 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE DEFAULT-UNARY-/))
 (8 4 (:DEFINITION FIX))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 )
(|(collect-* y x)|
 (5 3 (:REWRITE DEFAULT-*-2))
 (5 3 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(BUBBLE-DOWN)
(|(acl2-numberp (bubble-down x match))|
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-+-PROBLEM-FINDER
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-+-BUBBLE-DOWN
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-+-MATCH-1
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-+-MATCH-2
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-+-MATCH-3
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-*-PROBLEM-FINDER
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-*-BUBBLE-DOWN
 (7 5 (:REWRITE DEFAULT-*-1))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 5 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE FOLD-CONSTS-IN-*))
 )
(BUBBLE-DOWN-*-MATCH-1
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-*-MATCH-2
 (5 3 (:REWRITE DEFAULT-*-2))
 (5 3 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(BUBBLE-DOWN-*-MATCH-3
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
