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 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (16 16 (:REWRITE REDUCE-INTEGERP-+))
 (16 16 (:REWRITE INTEGERP-MINUS-X))
 (16 16 (:REWRITE |(equal (- x) (- y))|))
 (16 16 (:REWRITE |(< 0 (- x))|))
 (16 16 (:META META-INTEGERP-CORRECT))
 (14 14 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:LINEAR EXPT->-1-TWO))
 (10 10 (:LINEAR EXPT-<-1-ONE))
 (9 9 (:REWRITE |(* (- x) y)|))
 (6 6 (:REWRITE |(equal (+ c x) (+ d y))|))
 )
(PAIR-POW
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< d (+ c x))|))
 (1 1 (:REWRITE |(< (- x) 0)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(EXAMPLES)
(THEOREM-1
 (1008 336 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1008 336 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (672 336 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (672 336 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (672 336 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (672 336 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (387 57 (:REWRITE DEFAULT-*-2))
 (306 39 (:REWRITE DEFAULT-+-2))
 (305 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (234 9 (:LINEAR EXPT->-1-TWO))
 (234 9 (:LINEAR EXPT-<-1-ONE))
 (233 39 (:REWRITE DEFAULT-+-1))
 (227 65 (:REWRITE SIMPLIFY-SUMS-<))
 (227 65 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (227 65 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (225 9 (:LINEAR EXPT-X->=-X))
 (216 9 (:LINEAR EXPT-X->-X))
 (216 9 (:LINEAR EXPT->-1-ONE))
 (216 9 (:LINEAR EXPT-<-1-TWO))
 (200 65 (:REWRITE DEFAULT-<-2))
 (92 65 (:REWRITE DEFAULT-<-1))
 (68 24 (:REWRITE DEFAULT-CAR))
 (68 8 (:REWRITE |(equal (+ c x) d)|))
 (65 65 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (65 65 (:REWRITE |(< (- x) (- y))|))
 (60 57 (:REWRITE DEFAULT-*-1))
 (42 12 (:REWRITE DEFAULT-EXPT-1))
 (39 39 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (37 3 (:REWRITE |(equal (+ d x) (+ c y))|))
 (23 12 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE |(+ c (+ d x))|))
 (20 20 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (18 18 (:REWRITE |(< 0 (- x))|))
 (18 18 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (18 18 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (18 18 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (18 18 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (18 3 (:REWRITE |(equal (+ c x y) d)|))
 (14 14 (:REWRITE |(expt x (- n))|))
 (14 14 (:REWRITE |(expt 2^i n)|))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (7 7 (:REWRITE |(* (- x) y)|))
 (3 3 (:REWRITE |(equal (+ c x) (+ d y))|))
 )
(LEMMA-5-A)
(LEMMA-5-B
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE |(* c (* d x))|))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE DEFAULT-UNARY-/))
 (2 2 (:REWRITE |(* a (/ a) b)|))
 (2 2 (:REWRITE |(* 1 x)|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE |(< 0 (- x))|))
 )
(LEMMA-5-C
 (38 38 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (23 11 (:REWRITE SIMPLIFY-SUMS-<))
 (23 11 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (21 21 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (17 11 (:REWRITE DEFAULT-<-2))
 (17 11 (:REWRITE DEFAULT-<-1))
 (15 15 (:REWRITE |(< (- x) (- y))|))
 (14 14 (:REWRITE |(expt x (- n))|))
 (14 14 (:REWRITE |(expt 2^i n)|))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (10 10 (:REWRITE DEFAULT-EXPT-2))
 (10 10 (:REWRITE DEFAULT-EXPT-1))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (8 8 (:REWRITE DEFAULT-UNARY-/))
 (8 8 (:REWRITE |(< 0 (- x))|))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 6 (:REWRITE |(* c (* d x))|))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(LEMMA-5-D
 (30 12 (:REWRITE DEFAULT-*-2))
 (14 2 (:REWRITE SIMPLIFY-SUMS-<))
 (14 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (14 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (12 12 (:REWRITE DEFAULT-*-1))
 (8 2 (:REWRITE DEFAULT-<-2))
 (8 2 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (4 4 (:REWRITE DEFAULT-EXPT-2))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt x (- n))|))
 (4 4 (:REWRITE |(expt 2^i n)|))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 )
(LEMMA-5-E)
(LEMMA-5-F
 (58 4 (:LINEAR EXPT-X->=-X))
 (40 16 (:REWRITE SIMPLIFY-SUMS-<))
 (40 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (40 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (32 4 (:LINEAR EXPT-X->-X))
 (32 4 (:LINEAR EXPT->-1-ONE))
 (32 4 (:LINEAR EXPT-<-1-TWO))
 (30 12 (:REWRITE DEFAULT-*-2))
 (28 16 (:REWRITE DEFAULT-<-2))
 (28 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (12 12 (:REWRITE DEFAULT-*-1))
 (8 8 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:REWRITE DEFAULT-EXPT-1))
 (8 8 (:REWRITE |(expt x (- n))|))
 (8 8 (:REWRITE |(expt 2^i n)|))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (8 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (8 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (4 4 (:LINEAR EXPT->-1-TWO))
 (4 4 (:LINEAR EXPT-<-1-ONE))
 )
(LEMMA-5-G
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE |(* c (* d x))|))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE LEMMA-5-B))
 (2 2 (:REWRITE DEFAULT-UNARY-/))
 (2 2 (:REWRITE |(* a (/ a) b)|))
 (2 2 (:REWRITE |(* 1 x)|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE |(< 0 (- x))|))
 )
(LEMMA-5-H
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (39 39 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (39 39 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (39 39 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (39 39 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (9 5 (:REWRITE SIMPLIFY-SUMS-<))
 (9 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (9 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9 5 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (5 5 (:REWRITE DEFAULT-UNARY-/))
 (5 5 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE |(< 0 (- x))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE DEFAULT-*-2))
 (2 2 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(LEMMA-5-I
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (45 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (45 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (33 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-4G))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-3G))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-3C))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-2G))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-2C))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-1G))
 (21 21 (:TYPE-PRESCRIPTION NOT-INTEGERP-1C))
 (8 4 (:REWRITE SIMPLIFY-SUMS-<))
 (8 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (8 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (8 4 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (7 7 (:REWRITE DEFAULT-UNARY-/))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE |(< 0 (- x))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE |(* c (* d x))|))
 )
(LEMMA-5-J
 (38 38 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (29 17 (:REWRITE SIMPLIFY-SUMS-<))
 (29 17 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (23 17 (:REWRITE DEFAULT-<-2))
 (23 17 (:REWRITE DEFAULT-<-1))
 (21 21 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (21 21 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (21 21 (:REWRITE |(< (- x) (- y))|))
 (14 14 (:REWRITE |(expt x (- n))|))
 (14 14 (:REWRITE |(expt 2^i n)|))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (10 10 (:REWRITE DEFAULT-EXPT-2))
 (10 10 (:REWRITE DEFAULT-EXPT-1))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (8 8 (:REWRITE DEFAULT-UNARY-/))
 (8 8 (:REWRITE |(< 0 (- x))|))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 6 (:REWRITE |(* c (* d x))|))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(LEMMA-5-K
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (95 95 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (38 38 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (18 6 (:REWRITE DEFAULT-UNARY-/))
 (11 5 (:REWRITE SIMPLIFY-SUMS-<))
 (11 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (11 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (8 5 (:REWRITE DEFAULT-<-2))
 (8 5 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (6 6 (:REWRITE |(expt 2^i n)|))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE DEFAULT-EXPT-2))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt x (- n))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE |(< 0 (- x))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(LEMMA-5-L
 (348 2 (:REWRITE LEMMA-5-I))
 (86 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (52 52 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (52 4 (:LINEAR EXPT-X->=-X))
 (52 4 (:LINEAR EXPT-X->-X))
 (52 4 (:LINEAR EXPT->-1-ONE))
 (24 24 (:REWRITE |(expt 2^i n)|))
 (24 24 (:REWRITE |(expt 1/c n)|))
 (24 24 (:REWRITE |(expt (- x) n)|))
 (22 22 (:REWRITE DEFAULT-EXPT-2))
 (22 22 (:REWRITE DEFAULT-EXPT-1))
 (22 22 (:REWRITE |(expt x (- n))|))
 (18 6 (:REWRITE SIMPLIFY-SUMS-<))
 (18 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (18 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (18 6 (:REWRITE DEFAULT-UNARY-/))
 (12 6 (:REWRITE DEFAULT-<-2))
 (12 6 (:REWRITE DEFAULT-<-1))
 (10 10 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (8 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (4 4 (:LINEAR EXPT->-1-TWO))
 (4 4 (:LINEAR EXPT-<-1-TWO))
 (4 4 (:LINEAR EXPT-<-1-ONE))
 (4 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(LEMMA-5-M
 (592 5 (:REWRITE LEMMA-5-I))
 (161 161 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (161 161 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (161 161 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (145 145 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (145 145 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (81 33 (:REWRITE SIMPLIFY-SUMS-<))
 (81 33 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (81 33 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (70 70 (:REWRITE |(expt 2^i n)|))
 (70 70 (:REWRITE |(expt 1/c n)|))
 (70 70 (:REWRITE |(expt (- x) n)|))
 (68 68 (:REWRITE DEFAULT-EXPT-2))
 (68 68 (:REWRITE DEFAULT-EXPT-1))
 (68 68 (:REWRITE |(expt x (- n))|))
 (66 33 (:REWRITE DEFAULT-<-1))
 (60 12 (:REWRITE DEFAULT-UNARY-/))
 (50 50 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (50 50 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (50 50 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (50 50 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (48 33 (:REWRITE DEFAULT-<-2))
 (45 12 (:REWRITE DEFAULT-*-2))
 (44 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (44 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (42 24 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-4Q))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-4J))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-4G))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-4C))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3Q))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3L))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3J))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3G))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-3C))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2Q))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2L))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2J))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2G))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-2C))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1Q))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1L))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1J))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1G))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (35 35 (:TYPE-PRESCRIPTION NOT-INTEGERP-1C))
 (33 33 (:REWRITE |(< (- x) (- y))|))
 (33 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (30 12 (:LINEAR EXPT->-1-TWO))
 (30 12 (:LINEAR EXPT-<-1-ONE))
 (28 7 (:REWRITE DEFAULT-+-2))
 (26 12 (:LINEAR EXPT-<-1-TWO))
 (24 24 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (24 24 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (14 7 (:REWRITE DEFAULT-+-1))
 (13 4 (:REWRITE |(equal (+ c x) d)|))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (12 12 (:REWRITE DEFAULT-*-1))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (6 6 (:REWRITE |(< 0 (- x))|))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE |(* c (* d x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(LEMMA-5-N
 (68 68 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (32 32 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (23 7 (:REWRITE SIMPLIFY-SUMS-<))
 (23 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (15 7 (:REWRITE DEFAULT-<-2))
 (15 7 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE |(expt x (- n))|))
 (14 14 (:REWRITE |(expt 2^i n)|))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
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(PFIX)
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(THEOREM-2-C)
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(FIND-SMALLEST-Y-<=)
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 (3 3 (:REWRITE |(< (- x) 0)|))
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 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
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 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE |(< 0 (- x))|))
 )
(PAIR-POW-LOG-IS-LOGARITHMIC
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 (690 3 (:REWRITE |(equal (+ c x y) d)|))
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 (351 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (344 107 (:REWRITE NORMALIZE-ADDENDS))
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 (272 272 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
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 (120 120 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (112 16 (:REWRITE |(+ x (* c x))|))
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 (103 3 (:REWRITE |(+ (+ x y) z)|))
 (98 4 (:REWRITE |(+ y (+ x z))|))
 (97 11 (:REWRITE |(+ y x)|))
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 (67 7 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (61 19 (:REWRITE DEFAULT-UNARY-MINUS))
 (53 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (52 52 (:REWRITE |(* (- x) y)|))
 (45 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (34 2 (:REWRITE BUBBLE-DOWN-+-BUBBLE-DOWN))
 (31 27 (:REWRITE |(+ c (+ d x))|))
 (31 17 (:REWRITE REDUCE-INTEGERP-+))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
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 (30 30 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (29 4 (:REWRITE |(+ (* c x) (* d x))|))
 (23 23 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
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 (22 22 (:META META-INTEGERP-CORRECT))
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 (20 2 (:REWRITE |(+ x x)|))
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 (13 13 (:REWRITE |(equal (- x) (- y))|))
 (12 12 (:REWRITE FOLD-CONSTS-IN-+))
 (9 9 (:REWRITE |(integerp (* c x))|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (6 6 (:REWRITE |(< 0 (- x))|))
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 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (3 3 (:TYPE-PRESCRIPTION POSP))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4K))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3K))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2K))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1K))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(+ 0 x)|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (1 1 (:REWRITE |(equal (- x) 0)|))
 )
(PAIR-POW-2N-2N+1
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 (2240 1120 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
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 (36 36 (:REWRITE |(equal (+ c x y) d)|))
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 (22 22 (:REWRITE |(equal (+ c x) (+ d y))|))
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 )
(PAIR-POW-LOG-IS-CORRECT
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 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 )
