(*1)
(*2
 (18 12 (:REWRITE DEFAULT-*-1))
 (17 12 (:REWRITE DEFAULT-*-2))
 (11 11 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(*3)
(COMM2-TEST-1)
(PRIMEP)
(DIVIDES)
(QUOTIENT)
(MY-GCD)
(*1
 (8 2 (:LINEAR X*Y>1-POSITIVE))
 (3 3 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(*2
 (4 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 1 (:LINEAR X*Y>1-POSITIVE))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(*5)
(*6
 (12 3 (:LINEAR X*Y>1-POSITIVE))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(*7)
(*8
 (18 18 (:REWRITE DEFAULT-*-2))
 (18 18 (:REWRITE DEFAULT-*-1))
 (8 2 (:LINEAR X*Y>1-POSITIVE))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(*9)
(*10-SUFFICIENT)
(*12
 (2 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE FACT3))
 (1 1 (:REWRITE DEFAULT-*-1))
 )
(*10)
(*4)
(*3)
(PRIME-KEY)
(*1
 (275 63 (:REWRITE DEFAULT-*-2))
 (233 233 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (95 39 (:REWRITE DEFAULT-<-1))
 (87 63 (:REWRITE DEFAULT-*-1))
 (80 48 (:REWRITE DEFAULT-+-2))
 (80 48 (:REWRITE DEFAULT-+-1))
 (71 39 (:REWRITE DEFAULT-<-2))
 (58 8 (:LINEAR X*Y>1-POSITIVE))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (40 40 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 10 (:REWRITE ZIP-OPEN))
 (8 8 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (4 1 (:LINEAR EXPT->-1))
 (2 2 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 )
(*2
 (255 250 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (135 5 (:DEFINITION EXPT))
 (94 26 (:REWRITE DEFAULT-*-2))
 (62 26 (:REWRITE DEFAULT-*-1))
 (60 2 (:LINEAR X*Y>1-POSITIVE))
 (38 26 (:REWRITE DEFAULT-+-2))
 (38 26 (:REWRITE DEFAULT-+-1))
 (30 10 (:REWRITE COMMUTATIVITY-OF-+))
 (23 11 (:REWRITE DEFAULT-<-2))
 (19 11 (:REWRITE DEFAULT-<-1))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 2 (:LINEAR EXPT->-1))
 (5 5 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (5 5 (:REWRITE ZIP-OPEN))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 )
(*3
 (486 477 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (243 9 (:DEFINITION EXPT))
 (158 42 (:REWRITE DEFAULT-*-2))
 (94 42 (:REWRITE DEFAULT-*-1))
 (69 45 (:REWRITE DEFAULT-+-2))
 (69 45 (:REWRITE DEFAULT-+-1))
 (67 17 (:REWRITE DEFAULT-<-1))
 (60 2 (:LINEAR X*Y>1-POSITIVE))
 (54 18 (:REWRITE COMMUTATIVITY-OF-+))
 (37 17 (:REWRITE DEFAULT-<-2))
 (34 14 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (17 17 (:META CANCEL_PLUS-LESSP-CORRECT))
 (11 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (9 9 (:REWRITE ZIP-OPEN))
 (8 2 (:LINEAR EXPT->-1))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 )
(ABS-CHAIN-PROOF-1)
(*1
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (5 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(*2
 (162 6 (:DEFINITION EXPT))
 (110 30 (:REWRITE DEFAULT-*-2))
 (84 78 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (70 30 (:REWRITE DEFAULT-*-1))
 (69 37 (:REWRITE DEFAULT-+-2))
 (69 37 (:REWRITE DEFAULT-+-1))
 (47 15 (:REWRITE DEFAULT-UNARY-MINUS))
 (47 13 (:REWRITE DEFAULT-<-1))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:META CANCEL_PLUS-LESSP-CORRECT))
 (11 11 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6 6 (:REWRITE ZIP-OPEN))
 )
(*4
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 )
(*5
 (324 12 (:DEFINITION EXPT))
 (170 42 (:REWRITE DEFAULT-*-2))
 (161 149 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (93 61 (:REWRITE DEFAULT-+-2))
 (93 61 (:REWRITE DEFAULT-+-1))
 (82 42 (:REWRITE DEFAULT-*-1))
 (72 24 (:REWRITE COMMUTATIVITY-OF-+))
 (63 21 (:REWRITE DEFAULT-<-1))
 (47 15 (:REWRITE DEFAULT-UNARY-MINUS))
 (25 25 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (21 21 (:REWRITE DEFAULT-<-2))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 12 (:REWRITE ZIP-OPEN))
 )
(*6
 (30 2 (:LINEAR X*Y>1-POSITIVE))
 (24 10 (:REWRITE DEFAULT-<-2))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 10 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(*3)
(*7
 (7152 2666 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6123 1528 (:REWRITE DEFAULT-*-2))
 (3172 1528 (:REWRITE DEFAULT-*-1))
 (2202 1015 (:REWRITE DEFAULT-+-2))
 (2202 1015 (:REWRITE DEFAULT-+-1))
 (1952 766 (:REWRITE DEFAULT-<-1))
 (1324 420 (:REWRITE DEFAULT-UNARY-MINUS))
 (1204 21 (:REWRITE *-PRESERVES->=-FOR-NONNEGATIVES))
 (1128 766 (:REWRITE DEFAULT-<-2))
 (922 61 (:LINEAR X*Y>1-POSITIVE))
 (864 864 (:META CANCEL_PLUS-LESSP-CORRECT))
 (453 129 (:REWRITE ZIP-OPEN))
 (320 52 (:LINEAR EXPT->-1))
 (306 21 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (306 21 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 (191 83 (:REWRITE EQUAL-CONSTANT-+))
 (162 54 (:REWRITE FOLD-CONSTS-IN-+))
 (153 153 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (153 153 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (122 104 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (108 27 (:REWRITE <-0-+-NEGATIVE-1))
 (54 54 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (54 54 (:REWRITE EXPONENTS-ADD))
 )
(ABS-CHAIN-PROOF-2)
(*1
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (5 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(*2
 (162 6 (:DEFINITION EXPT))
 (110 30 (:REWRITE DEFAULT-*-2))
 (84 78 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (70 30 (:REWRITE DEFAULT-*-1))
 (69 37 (:REWRITE DEFAULT-+-2))
 (69 37 (:REWRITE DEFAULT-+-1))
 (47 15 (:REWRITE DEFAULT-UNARY-MINUS))
 (47 13 (:REWRITE DEFAULT-<-1))
 (36 12 (:REWRITE COMMUTATIVITY-OF-+))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:META CANCEL_PLUS-LESSP-CORRECT))
 (11 11 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6 6 (:REWRITE ZIP-OPEN))
 )
(*4)
(*6
 (540 20 (:DEFINITION EXPT))
 (403 383 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (310 78 (:REWRITE DEFAULT-*-2))
 (158 78 (:REWRITE DEFAULT-*-1))
 (120 40 (:REWRITE COMMUTATIVITY-OF-+))
 (100 84 (:REWRITE DEFAULT-+-2))
 (100 84 (:REWRITE DEFAULT-+-1))
 (100 36 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (92 52 (:REWRITE DEFAULT-<-2))
 (68 52 (:REWRITE DEFAULT-<-1))
 (60 60 (:META CANCEL_PLUS-LESSP-CORRECT))
 (60 2 (:LINEAR X*Y>1-POSITIVE))
 (50 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (20 20 (:REWRITE ZIP-OPEN))
 (8 8 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (8 8 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (8 2 (:LINEAR EXPT->-1))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 )
(*5)
(*3)
(*7
 (7152 2666 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6123 1528 (:REWRITE DEFAULT-*-2))
 (3172 1528 (:REWRITE DEFAULT-*-1))
 (2202 1015 (:REWRITE DEFAULT-+-2))
 (2202 1015 (:REWRITE DEFAULT-+-1))
 (1952 766 (:REWRITE DEFAULT-<-1))
 (1324 420 (:REWRITE DEFAULT-UNARY-MINUS))
 (1204 21 (:REWRITE *-PRESERVES->=-FOR-NONNEGATIVES))
 (1128 766 (:REWRITE DEFAULT-<-2))
 (922 61 (:LINEAR X*Y>1-POSITIVE))
 (864 864 (:META CANCEL_PLUS-LESSP-CORRECT))
 (453 129 (:REWRITE ZIP-OPEN))
 (320 52 (:LINEAR EXPT->-1))
 (306 21 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (306 21 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 (191 83 (:REWRITE EQUAL-CONSTANT-+))
 (162 54 (:REWRITE FOLD-CONSTS-IN-+))
 (153 153 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (153 153 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (122 104 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (108 27 (:REWRITE <-0-+-NEGATIVE-1))
 (54 54 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (54 54 (:REWRITE EXPONENTS-ADD))
 )
(ABS-CHAIN-PROOF-3)
