(O)
(INX)
(UNBUNDLE)
(ARGS-SYNTAX-GUARD)
(GENERATE-OPEN-THEOREMS)
(IF-FORMP
 (152 72 (:REWRITE DEFAULT-+-2))
 (97 72 (:REWRITE DEFAULT-+-1))
 (48 12 (:DEFINITION INTEGER-ABS))
 (48 6 (:DEFINITION LENGTH))
 (45 45 (:REWRITE DEFAULT-CDR))
 (30 6 (:DEFINITION LEN))
 (21 16 (:REWRITE DEFAULT-<-2))
 (20 16 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:REWRITE DEFAULT-REALPART))
 (6 6 (:REWRITE DEFAULT-NUMERATOR))
 (6 6 (:REWRITE DEFAULT-IMAGPART))
 (6 6 (:REWRITE DEFAULT-DENOMINATOR))
 (6 6 (:REWRITE DEFAULT-COERCE-2))
 (6 6 (:REWRITE DEFAULT-COERCE-1))
 )
(IF-TEST
 (267 125 (:REWRITE DEFAULT-+-2))
 (169 125 (:REWRITE DEFAULT-+-1))
 (104 26 (:REWRITE COMMUTATIVITY-OF-+))
 (104 26 (:DEFINITION INTEGER-ABS))
 (104 13 (:DEFINITION LENGTH))
 (65 13 (:DEFINITION LEN))
 (41 32 (:REWRITE DEFAULT-<-2))
 (36 32 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (13 13 (:REWRITE DEFAULT-REALPART))
 (13 13 (:REWRITE DEFAULT-NUMERATOR))
 (13 13 (:REWRITE DEFAULT-IMAGPART))
 (13 13 (:REWRITE DEFAULT-DENOMINATOR))
 (13 13 (:REWRITE DEFAULT-COERCE-2))
 (13 13 (:REWRITE DEFAULT-COERCE-1))
 )
(IF-BASE
 (267 125 (:REWRITE DEFAULT-+-2))
 (169 125 (:REWRITE DEFAULT-+-1))
 (104 26 (:REWRITE COMMUTATIVITY-OF-+))
 (104 26 (:DEFINITION INTEGER-ABS))
 (104 13 (:DEFINITION LENGTH))
 (65 13 (:DEFINITION LEN))
 (41 32 (:REWRITE DEFAULT-<-2))
 (36 32 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (13 13 (:REWRITE DEFAULT-REALPART))
 (13 13 (:REWRITE DEFAULT-NUMERATOR))
 (13 13 (:REWRITE DEFAULT-IMAGPART))
 (13 13 (:REWRITE DEFAULT-DENOMINATOR))
 (13 13 (:REWRITE DEFAULT-COERCE-2))
 (13 13 (:REWRITE DEFAULT-COERCE-1))
 )
(IF-BODY
 (267 125 (:REWRITE DEFAULT-+-2))
 (169 125 (:REWRITE DEFAULT-+-1))
 (104 26 (:REWRITE COMMUTATIVITY-OF-+))
 (104 26 (:DEFINITION INTEGER-ABS))
 (104 13 (:DEFINITION LENGTH))
 (65 13 (:DEFINITION LEN))
 (41 32 (:REWRITE DEFAULT-<-2))
 (36 32 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (13 13 (:REWRITE DEFAULT-REALPART))
 (13 13 (:REWRITE DEFAULT-NUMERATOR))
 (13 13 (:REWRITE DEFAULT-IMAGPART))
 (13 13 (:REWRITE DEFAULT-DENOMINATOR))
 (13 13 (:REWRITE DEFAULT-COERCE-2))
 (13 13 (:REWRITE DEFAULT-COERCE-1))
 )
(CONTAINS-FAPP-REC)
(WF-MEASURE-BODY)
(REMAP-FN-REC)
(REPLACE-FN-REC)
(MAP-REPLACE-FN
 (1 1 (:TYPE-PRESCRIPTION REPLACE-FN-REC))
 )
(TRUE-LISTP-MAP-REPLACE-FN)
(EXTRACT-FN)
(PUSH-LETS)
(TEST-BASE-BODY)
(PUN-FORM)
(FIRST-LIST)
(CONTAINS-GUARD-DECLARATION-REC)
(CONTAINS-GUARD-DECLARATION)
(CONTAIN-GUARD-DECLARATIONS)
(INCA)
(SOME-TEST)
(TEST-A)
(FOOBASE_BODY_1)
(FOOTEST_BODY_1)
(FOOTEST_BODY_1_TYPE)
(FOOSTEP_BODY_1)
(FOOBASE_BODY)
(FOOTEST_BODY)
(FOOSTEP_BODY)
(|FOO_1_MINTERM-pun-stn|)
(|FOO_1_MINTERM-pun-fch-prop|)
(FOO_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |FOO_1_MINTERM-pun-stn|))
 )
(FOO_1_MINTERM_TERM_TYPE)
(|FOO_1_MINTERM-xtesq|)
(|FOO_1_MINTERM-xbasq|)
(|FOO_1_MINTERM-xsteq|)
(|FOO_1_MINTERM-xun-stn|)
(|FOO_1_MINTERM-xun-fch-fn|)
(|FOO_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|FOO_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |FOO_1_MINTERM-xun-stn|))
 )
(|FOO_1_MINTERM_pun|)
(FOO_1_MINTERM)
(|FOO_1_MINTERM_FOO_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|FOO_1_MINTERM_pun_def|)
(FOO_1_MINTERM_PROP
 (14 2 (:DEFINITION |FOO_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |FOO_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-FOO_1_MINTERM)
(NATP_FOO_1_MINTERM)
(FOO_1_MINTERM_TERM_PROP)
(FOO_1_MEASURE)
(FOO_1_TERMINATES)
(FOO_1_TERMINATES_TYPE)
(OPEN_FOO_1_MEASURE
 (7 7 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_1_TERMINATES)
(FOO_MEASURE)
(FOO_TERMINATES)
(FOO_TERMINATES_TYPE)
(OPEN_FOO_MEASURE
 (20 4 (:REWRITE OPEN_FOO_1_TERMINATES))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_MEASURE!)
(OPEN_FOO_TERMINATES
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(OPEN_FOO_TERMINATES!
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(FOO
 (19 19 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_REC_TERM
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(INTEGERP-FOO)
(FOO-PROP
 (42 42 (:REWRITE DEFAULT-+-2))
 (42 42 (:REWRITE DEFAULT-+-1))
 (30 16 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-CAR))
 (19 16 (:REWRITE DEFAULT-<-1))
 )
(FOO_TEST)
(FOO_BASE
 (1 1 (:TYPE-PRESCRIPTION FOO_BASE))
 )
(FOO_STEP1
 (1 1 (:TYPE-PRESCRIPTION FOO_STEP1))
 )
(BOOLEANP_FOO_TEST)
(|FOO_MINTERM-pun-stn|
 (6 6 (:TYPE-PRESCRIPTION FOO_STEP1))
 )
(|FOO_MINTERM-pun-fch-prop|)
(FOO_MINTERM_TERM)
(FOO_MINTERM_TERM_TYPE)
(|FOO_MINTERM-xtesq|)
(|FOO_MINTERM-xbasq|)
(|FOO_MINTERM-xsteq|
 (1 1 (:TYPE-PRESCRIPTION FOO_STEP1))
 )
(|FOO_MINTERM-xun-stn|)
(|FOO_MINTERM-xun-fch-fn|)
(|FOO_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|FOO_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |FOO_MINTERM-xun-stn|))
 )
(|FOO_MINTERM_pun|)
(FOO_MINTERM)
(|FOO_MINTERM_FOO_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|FOO_MINTERM_pun_def|
 (1 1 (:TYPE-PRESCRIPTION FOO_STEP1))
 )
(FOO_MINTERM_PROP
 (14 2 (:DEFINITION |FOO_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |FOO_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-FOO_MINTERM)
(NATP_FOO_MINTERM)
(FOO_MINTERM_TERM_PROP)
(FOO_MEASURE)
(FOO_TERMINATES)
(FOO_TERMINATES_TYPE)
(OPEN_FOO_MEASURE
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_TERMINATES)
(DEFXCH_R0)
(DEFXCH_DEFAULT)
(DEFXCH_TEST)
(DEFXCH_STEPS
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 )
(DEFXCH_HYPS)
(DEFXCH_TYPE)
(DEFXCH_INC)
(DEFXCH_BASE)
(DEFXCHBASE_BODY_1)
(DEFXCHTEST_BODY_1)
(DEFXCHTEST_BODY_1_TYPE)
(DEFXCHSTEP_BODY_1
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 )
(DEFXCHBASE_BODY)
(DEFXCHTEST_BODY)
(DEFXCHSTEP_BODY)
(|DEFXCH_1_MINTERM-pun-stn|)
(|DEFXCH_1_MINTERM-pun-fch-prop|)
(DEFXCH_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |DEFXCH_1_MINTERM-pun-stn|))
 )
(DEFXCH_1_MINTERM_TERM_TYPE)
(|DEFXCH_1_MINTERM-xtesq|)
(|DEFXCH_1_MINTERM-xbasq|)
(|DEFXCH_1_MINTERM-xsteq|)
(|DEFXCH_1_MINTERM-xun-stn|)
(|DEFXCH_1_MINTERM-xun-fch-fn|)
(|DEFXCH_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|DEFXCH_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |DEFXCH_1_MINTERM-xun-stn|))
 )
(|DEFXCH_1_MINTERM_pun|)
(DEFXCH_1_MINTERM)
(|DEFXCH_1_MINTERM_DEFXCH_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|DEFXCH_1_MINTERM_pun_def|)
(DEFXCH_1_MINTERM_PROP
 (14 2 (:DEFINITION |DEFXCH_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |DEFXCH_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-DEFXCH_1_MINTERM)
(NATP_DEFXCH_1_MINTERM)
(DEFXCH_1_MINTERM_TERM_PROP)
(DEFXCH_1_MEASURE)
(DEFXCH_1_TERMINATES)
(DEFXCH_1_TERMINATES_TYPE)
(OPEN_DEFXCH_1_MEASURE
 (7 7 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_DEFXCH_1_TERMINATES)
(DEFXCH_MEASURE)
(DEFXCH_TERMINATES)
(DEFXCH_TERMINATES_TYPE)
(OPEN_DEFXCH_MEASURE
 (20 4 (:REWRITE OPEN_DEFXCH_1_TERMINATES))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_DEFXCH_MEASURE!)
(OPEN_DEFXCH_TERMINATES
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(OPEN_DEFXCH_TERMINATES!
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(DEFXCH
 (19 19 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_DEFXCH_REC_TERM
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(|DEFXCH_FN_PUN-arity-1-test|)
(|DEFXCH_FN_PUN-arity-1-base|)
(|DEFXCH_FN_PUN-arity-1-step|
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_INC))
 )
(|DEFXCH_FN_PUN-arity-1-type|)
(|DEFXCH_FN_PUN-arity-1-stn|)
(|DEFXCH_FN_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|DEFXCH_FN_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |DEFXCH_FN_PUN-arity-1-stn|))
 )
(|DEFXCH_FN_PUN-arity-1-CLIQUE|)
(|DEFXCH_FN_PUN-arity-1-DEF|)
(|DEFXCH_FN_PUN-arity-1-TYPE|)
(DEFXCH_FN_PUN)
(DEFXCH_FN_PUN-DEF
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:TYPE-PRESCRIPTION DEFXCH_BASE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_INC))
 )
(OPEN-DEFXCH_FN_PUN)
(DEFXCH_BASE_DEFXCH_INC_COMMUTE
 (9 6 (:TYPE-PRESCRIPTION DEFXCH_INC))
 (9 6 (:TYPE-PRESCRIPTION DEFXCH_BASE))
 )
(DEFXCH_TYPE_DEFXCH_R0)
(DEFXCH_TYPE_DEFXCH_BASE)
(DEFXCH_TYPE_DEFXCH_DEFAULT)
(DEFXCH_INC_PRESERVES_TYPE)
(DEFXCH_STEPS_PRESERVES_HYPS)
(NATP-DEFXCH_MEASURE)
(DEFXCH_MEASURE_PROPERTY
 (17 17 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(DEFXCH_TERMINATES_PROPERTY
 (5 5 (:REWRITE DEFAULT-CAR))
 )
(DEFXCH_FN_PUN_PROP
 (4 4 (:TYPE-PRESCRIPTION DEFXCH_BASE))
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_STEPS))
 (1 1 (:TYPE-PRESCRIPTION DEFXCH_INC))
 )
(DEFXCH_INC_OF-INC
 (12 12 (:TYPE-PRESCRIPTION DEFXCH_INC))
 )
(DEFXCH_INDUCTSHUN
 (4 4 (:REWRITE DEFXCH_STEPS_PRESERVES_HYPS))
 )
(OPEN_DEFXCH_FN_PUN
 (4 4 (:REWRITE DEFXCH_STEPS_PRESERVES_HYPS))
 (4 2 (:REWRITE DEFXCH_INC_OF-INC))
 (2 2 (:REWRITE DEFXCH_INC_PRESERVES_TYPE))
 (2 2 (:REWRITE DEFXCH_BASE_DEFXCH_INC_COMMUTE))
 )
(FOO-OVER-DEFXCH_INC
 (60 4 (:DEFINITION DEFXCH_FN_PUN_PROP))
 )
(TERMINAL_PROP
 (54 6 (:DEFINITION DEFXCH_FN_PUN_PROP))
 (3 1 (:REWRITE DEFXCH_INC_OF-INC))
 )
(DEFXCH_FN
 (2 2 (:REWRITE DEFXCH_TERMINATES_PROPERTY))
 )
(DEFXCH_AUX)
(OPEN_DEFXCH_AUX)
(DEFXCH_FN_TO_AUX
 (6 2 (:REWRITE DEFXCH_INC_PRESERVES_TYPE))
 )
(DEFXCH_FN_TO_FN_PUN
 (33 4 (:DEFINITION DEFXCH_FN_PUN_PROP))
 (11 4 (:REWRITE DEFXCH_INC_PRESERVES_TYPE))
 )
(TEST)
(FOO_INDUCTIONBASE_BODY_1)
(FOO_INDUCTIONTEST_BODY_1)
(FOO_INDUCTIONTEST_BODY_1_TYPE)
(FOO_INDUCTIONSTEP_BODY_1)
(FOO_INDUCTIONBASE_BODY)
(FOO_INDUCTIONTEST_BODY)
(FOO_INDUCTIONSTEP_BODY)
(|FOO_INDUCTION_1_MINTERM-pun-stn|)
(|FOO_INDUCTION_1_MINTERM-pun-fch-prop|)
(FOO_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |FOO_INDUCTION_1_MINTERM-pun-stn|))
 )
(FOO_INDUCTION_1_MINTERM_TERM_TYPE)
(|FOO_INDUCTION_1_MINTERM-xtesq|)
(|FOO_INDUCTION_1_MINTERM-xbasq|)
(|FOO_INDUCTION_1_MINTERM-xsteq|)
(|FOO_INDUCTION_1_MINTERM-xun-stn|)
(|FOO_INDUCTION_1_MINTERM-xun-fch-fn|)
(|FOO_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|FOO_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |FOO_INDUCTION_1_MINTERM-xun-stn|))
 )
(|FOO_INDUCTION_1_MINTERM_pun|)
(FOO_INDUCTION_1_MINTERM)
(|FOO_INDUCTION_1_MINTERM_FOO_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|FOO_INDUCTION_1_MINTERM_pun_def|)
(FOO_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |FOO_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |FOO_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-FOO_INDUCTION_1_MINTERM)
(NATP_FOO_INDUCTION_1_MINTERM)
(FOO_INDUCTION_1_MINTERM_TERM_PROP)
(FOO_INDUCTION_1_MEASURE)
(FOO_INDUCTION_1_TERMINATES)
(FOO_INDUCTION_1_TERMINATES_TYPE)
(OPEN_FOO_INDUCTION_1_MEASURE
 (7 7 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_INDUCTION_1_TERMINATES)
(FOO_INDUCTION_MEASURE)
(FOO_INDUCTION_TERMINATES)
(FOO_INDUCTION_TERMINATES_TYPE)
(OPEN_FOO_INDUCTION_MEASURE
 (20 4 (:REWRITE OPEN_FOO_INDUCTION_1_TERMINATES))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_INDUCTION_MEASURE!)
(OPEN_FOO_INDUCTION_TERMINATES
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(OPEN_FOO_INDUCTION_TERMINATES!
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(FOO_INDUCTION
 (19 19 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_FOO_INDUCTION_REC_TERM
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(|FOO_PUN-arity-1-test|)
(|FOO_PUN-arity-1-base|)
(|FOO_PUN-arity-1-step|)
(|FOO_PUN-arity-1-type|)
(|FOO_PUN-arity-1-stn|)
(|FOO_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|FOO_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |FOO_PUN-arity-1-stn|))
 )
(|FOO_PUN-arity-1-CLIQUE|)
(|FOO_PUN-arity-1-DEF|)
(|FOO_PUN-arity-1-TYPE|)
(FOO_PUN)
(FOO_PUN-DEF
 (6 6 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN-FOO_PUN)
(FOO
 (19 19 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(FOO_TO_FOO_PUN
 (28 28 (:REWRITE DEFAULT-CAR))
 (24 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (8 2 (:REWRITE FOLD-CONSTS-IN-+))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(GOO_TEST)
(GOO_STEP)
(GOO_PRED)
(GOO_BASE)
(GOO_INC)
(GOO_INDUCTIONBASE_BODY_1)
(GOO_INDUCTIONTEST_BODY_1)
(GOO_INDUCTIONTEST_BODY_1_TYPE)
(GOO_INDUCTIONSTEP_BODY_1)
(GOO_INDUCTIONBASE_BODY)
(GOO_INDUCTIONTEST_BODY)
(GOO_INDUCTIONSTEP_BODY)
(|GOO_INDUCTION_1_MINTERM-pun-stn|)
(|GOO_INDUCTION_1_MINTERM-pun-fch-prop|)
(GOO_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |GOO_INDUCTION_1_MINTERM-pun-stn|))
 )
(GOO_INDUCTION_1_MINTERM_TERM_TYPE)
(|GOO_INDUCTION_1_MINTERM-xtesq|)
(|GOO_INDUCTION_1_MINTERM-xbasq|)
(|GOO_INDUCTION_1_MINTERM-xsteq|)
(|GOO_INDUCTION_1_MINTERM-xun-stn|)
(|GOO_INDUCTION_1_MINTERM-xun-fch-fn|)
(|GOO_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOO_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |GOO_INDUCTION_1_MINTERM-xun-stn|))
 )
(|GOO_INDUCTION_1_MINTERM_pun|)
(GOO_INDUCTION_1_MINTERM)
(|GOO_INDUCTION_1_MINTERM_GOO_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|GOO_INDUCTION_1_MINTERM_pun_def|)
(GOO_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |GOO_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |GOO_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-GOO_INDUCTION_1_MINTERM)
(NATP_GOO_INDUCTION_1_MINTERM)
(GOO_INDUCTION_1_MINTERM_TERM_PROP)
(GOO_INDUCTION_1_MEASURE)
(GOO_INDUCTION_1_TERMINATES)
(GOO_INDUCTION_1_TERMINATES_TYPE)
(OPEN_GOO_INDUCTION_1_MEASURE
 (7 7 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOO_INDUCTION_1_TERMINATES)
(GOO_INDUCTION_MEASURE)
(GOO_INDUCTION_TERMINATES)
(GOO_INDUCTION_TERMINATES_TYPE)
(OPEN_GOO_INDUCTION_MEASURE
 (20 4 (:REWRITE OPEN_GOO_INDUCTION_1_TERMINATES))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOO_INDUCTION_MEASURE!)
(OPEN_GOO_INDUCTION_TERMINATES
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(OPEN_GOO_INDUCTION_TERMINATES!
 (10 10 (:REWRITE DEFAULT-CAR))
 )
(GOO_INDUCTION
 (19 19 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOO_INDUCTION_REC_TERM
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(|GOO_PUN-arity-1-test|)
(|GOO_PUN-arity-1-base|)
(|GOO_PUN-arity-1-step|
 (1 1 (:TYPE-PRESCRIPTION GOO_INC))
 )
(|GOO_PUN-arity-1-type|)
(|GOO_PUN-arity-1-stn|)
(|GOO_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOO_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOO_PUN-arity-1-stn|))
 )
(|GOO_PUN-arity-1-CLIQUE|)
(|GOO_PUN-arity-1-DEF|)
(|GOO_PUN-arity-1-TYPE|)
(GOO_PUN)
(GOO_PUN-DEF
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:TYPE-PRESCRIPTION GOO_BASE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (1 1 (:TYPE-PRESCRIPTION GOO_INC))
 )
(OPEN-GOO_PUN)
(GOO
 (19 19 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(GOO_TO_GOO_PUN
 (28 28 (:REWRITE DEFAULT-CAR))
 (24 6 (:DEFINITION GOO_PUN-DEF))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(JUST-BODY)
(TAIL-BODY
 (267 125 (:REWRITE DEFAULT-+-2))
 (169 125 (:REWRITE DEFAULT-+-1))
 (104 26 (:REWRITE COMMUTATIVITY-OF-+))
 (104 26 (:DEFINITION INTEGER-ABS))
 (104 13 (:DEFINITION LENGTH))
 (65 13 (:DEFINITION LEN))
 (41 32 (:REWRITE DEFAULT-<-2))
 (36 32 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (13 13 (:REWRITE DEFAULT-REALPART))
 (13 13 (:REWRITE DEFAULT-NUMERATOR))
 (13 13 (:REWRITE DEFAULT-IMAGPART))
 (13 13 (:REWRITE DEFAULT-DENOMINATOR))
 (13 13 (:REWRITE DEFAULT-COERCE-2))
 (13 13 (:REWRITE DEFAULT-COERCE-1))
 )
(TEXT)
(HOOT)
(STX)
(STY)
(INXX)
(GOOP_INDUCTIONBASE_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1_TYPE)
(GOOP_INDUCTIONSTEP_BODY_1)
(GOOP_INDUCTIONBASE_BODY)
(GOOP_INDUCTIONTEST_BODY)
(GOOP_INDUCTIONSTEP_BODY)
(|GOOP_INDUCTION_1_MINTERM-pun-stn|)
(|GOOP_INDUCTION_1_MINTERM-pun-fch-prop|)
(GOOP_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 )
(GOOP_INDUCTION_1_MINTERM_TERM_TYPE)
(|GOOP_INDUCTION_1_MINTERM-xtesq|)
(|GOOP_INDUCTION_1_MINTERM-xbasq|)
(|GOOP_INDUCTION_1_MINTERM-xsteq|)
(|GOOP_INDUCTION_1_MINTERM-xun-stn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fch-fn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-xun-stn|))
 )
(|GOOP_INDUCTION_1_MINTERM_pun|)
(GOOP_INDUCTION_1_MINTERM)
(|GOOP_INDUCTION_1_MINTERM_GOOP_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|GOOP_INDUCTION_1_MINTERM_pun_def|)
(GOOP_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |GOOP_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-GOOP_INDUCTION_1_MINTERM)
(NATP_GOOP_INDUCTION_1_MINTERM)
(GOOP_INDUCTION_1_MINTERM_TERM_PROP)
(GOOP_INDUCTION_1_MEASURE)
(GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_1_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_1_MEASURE
 (14 14 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_MEASURE)
(GOOP_INDUCTION_TERMINATES)
(GOOP_INDUCTION_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_MEASURE
 (36 4 (:REWRITE OPEN_GOOP_INDUCTION_1_TERMINATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_MEASURE!)
(OPEN_GOOP_INDUCTION_TERMINATES
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_X
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_Y
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES!
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(GOOP_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_REC_TERM
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 )
(|GOOP_PUN-arity-1-test|)
(|GOOP_PUN-arity-1-base|)
(|GOOP_PUN-arity-1-step|)
(|GOOP_PUN-arity-1-type|)
(|GOOP_PUN-arity-1-stn|)
(|GOOP_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_PUN-arity-1-stn|))
 )
(|GOOP_PUN-arity-1-CLIQUE|)
(|GOOP_PUN-arity-1-DEF|)
(|GOOP_PUN-arity-1-TYPE|)
(GOOP_PUN)
(GOOP_PUN-DEF
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP_PUN)
(GOOP
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-test-1|)
(|GOOP-step-1|)
(|GOOP-inc-1|)
(|GOOP-measure-1|)
(|GOOP-terminates-1|)
(|GOOP-1_PUN-arity-1-test|)
(|GOOP-1_PUN-arity-1-base|)
(|GOOP-1_PUN-arity-1-step|)
(|GOOP-1_PUN-arity-1-type|)
(|GOOP-1_PUN-arity-1-stn|)
(|GOOP-1_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP-1_PUN-arity-1-stn|))
 )
(|GOOP-1_PUN-arity-1-CLIQUE|)
(|GOOP-1_PUN-arity-1-DEF|)
(|GOOP-1_PUN-arity-1-TYPE|)
(GOOP-1_PUN)
(GOOP-1_PUN-DEF
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP-1_PUN)
(GOOP-1
 (22 22 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(GOOP-1_TO_GOOP-1_PUN
 (140 4 (:DEFINITION GOOP-1_PUN-DEF))
 (45 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (19 19 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(|GOOP-1-reduction|
 (68 68 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(GOOP_PUN_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1-pun-reduction|
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (20 2 (:DEFINITION GOOP_PUN-DEF))
 (18 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:TYPE-PRESCRIPTION GOOP_PUN_INDUCTION))
 )
(|GOOP_to_GOOP_pun|
 (70 2 (:DEFINITION GOOP-1_PUN-DEF))
 (42 6 (:DEFINITION |GOOP-test-1|))
 (40 4 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (38 6 (:REWRITE OPEN-GOOP-1_PUN))
 (32 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY))
 (30 30 (:REWRITE DEFAULT-CAR))
 (28 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY_1))
 (22 2 (:DEFINITION |GOOP-inc-1|))
 (15 15 (:REWRITE DEFAULT-CDR))
 (14 2 (:DEFINITION |GOOP-step-1|))
 (8 2 (:DEFINITION INXX))
 (4 4 (:TYPE-PRESCRIPTION GOOP_INDUCTIONTEST_BODY))
 (4 4 (:TYPE-PRESCRIPTION |GOOP-test-1|))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(TEXT)
(HOOT)
(STX)
(STY)
(INXX)
(GOOP_INDUCTIONBASE_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1_TYPE)
(GOOP_INDUCTIONSTEP_BODY_1)
(GOOP_INDUCTIONBASE_BODY)
(GOOP_INDUCTIONTEST_BODY)
(GOOP_INDUCTIONSTEP_BODY)
(|GOOP_INDUCTION_1_MINTERM-pun-stn|)
(|GOOP_INDUCTION_1_MINTERM-pun-fch-prop|)
(GOOP_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 )
(GOOP_INDUCTION_1_MINTERM_TERM_TYPE)
(|GOOP_INDUCTION_1_MINTERM-xtesq|)
(|GOOP_INDUCTION_1_MINTERM-xbasq|)
(|GOOP_INDUCTION_1_MINTERM-xsteq|)
(|GOOP_INDUCTION_1_MINTERM-xun-stn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fch-fn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-xun-stn|))
 )
(|GOOP_INDUCTION_1_MINTERM_pun|)
(GOOP_INDUCTION_1_MINTERM)
(|GOOP_INDUCTION_1_MINTERM_GOOP_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|GOOP_INDUCTION_1_MINTERM_pun_def|)
(GOOP_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |GOOP_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-GOOP_INDUCTION_1_MINTERM)
(NATP_GOOP_INDUCTION_1_MINTERM)
(GOOP_INDUCTION_1_MINTERM_TERM_PROP)
(GOOP_INDUCTION_1_MEASURE)
(GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_1_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_1_MEASURE
 (14 14 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_MEASURE)
(GOOP_INDUCTION_TERMINATES)
(GOOP_INDUCTION_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_MEASURE
 (36 4 (:REWRITE OPEN_GOOP_INDUCTION_1_TERMINATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_MEASURE!)
(OPEN_GOOP_INDUCTION_TERMINATES
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_X
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_Y
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES!
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(GOOP_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_REC_TERM
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 )
(|GOOP_PUN-arity-1-test|)
(|GOOP_PUN-arity-1-base|)
(|GOOP_PUN-arity-1-step|)
(|GOOP_PUN-arity-1-type|)
(|GOOP_PUN-arity-1-stn|)
(|GOOP_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_PUN-arity-1-stn|))
 )
(|GOOP_PUN-arity-1-CLIQUE|)
(|GOOP_PUN-arity-1-DEF|)
(|GOOP_PUN-arity-1-TYPE|)
(GOOP_PUN)
(GOOP_PUN-DEF
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP_PUN)
(GOOP
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-test-1|)
(|GOOP-step-1|)
(|GOOP-inc-1|)
(|GOOP-measure-1|)
(|GOOP-terminates-1|)
(|GOOP-1_PUN-arity-1-test|)
(|GOOP-1_PUN-arity-1-base|)
(|GOOP-1_PUN-arity-1-step|)
(|GOOP-1_PUN-arity-1-type|)
(|GOOP-1_PUN-arity-1-stn|)
(|GOOP-1_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP-1_PUN-arity-1-stn|))
 )
(|GOOP-1_PUN-arity-1-CLIQUE|)
(|GOOP-1_PUN-arity-1-DEF|)
(|GOOP-1_PUN-arity-1-TYPE|)
(GOOP-1_PUN)
(GOOP-1_PUN-DEF
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP-1_PUN)
(GOOP-1
 (22 22 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(GOOP-1_TO_GOOP-1_PUN
 (140 4 (:DEFINITION GOOP-1_PUN-DEF))
 (45 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (19 19 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(|GOOP-1-reduction|
 (70 70 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE DEFAULT-CDR))
 (6 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE DEFAULT-+-1))
 )
(GOOP_PUN_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1-pun-reduction|
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (20 2 (:DEFINITION GOOP_PUN-DEF))
 (18 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:TYPE-PRESCRIPTION GOOP_PUN_INDUCTION))
 )
(|GOOP_to_GOOP_pun|
 (70 2 (:DEFINITION GOOP-1_PUN-DEF))
 (42 6 (:DEFINITION |GOOP-test-1|))
 (40 4 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (38 6 (:REWRITE OPEN-GOOP-1_PUN))
 (32 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY))
 (30 30 (:REWRITE DEFAULT-CAR))
 (28 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY_1))
 (22 2 (:DEFINITION |GOOP-inc-1|))
 (15 15 (:REWRITE DEFAULT-CDR))
 (14 2 (:DEFINITION |GOOP-step-1|))
 (8 2 (:DEFINITION INXX))
 (4 4 (:TYPE-PRESCRIPTION GOOP_INDUCTIONTEST_BODY))
 (4 4 (:TYPE-PRESCRIPTION |GOOP-test-1|))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(TEXT)
(HOOT)
(STX)
(STY)
(INXX)
(GOOP_INDUCTIONBASE_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1)
(GOOP_INDUCTIONTEST_BODY_1_TYPE)
(GOOP_INDUCTIONSTEP_BODY_1)
(GOOP_INDUCTIONBASE_BODY)
(GOOP_INDUCTIONTEST_BODY)
(GOOP_INDUCTIONSTEP_BODY)
(|GOOP_INDUCTION_1_MINTERM-pun-stn|)
(|GOOP_INDUCTION_1_MINTERM-pun-fch-prop|)
(GOOP_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 )
(GOOP_INDUCTION_1_MINTERM_TERM_TYPE)
(|GOOP_INDUCTION_1_MINTERM-xtesq|)
(|GOOP_INDUCTION_1_MINTERM-xbasq|)
(|GOOP_INDUCTION_1_MINTERM-xsteq|)
(|GOOP_INDUCTION_1_MINTERM-xun-stn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fch-fn|)
(|GOOP_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_INDUCTION_1_MINTERM-xun-stn|))
 )
(|GOOP_INDUCTION_1_MINTERM_pun|)
(GOOP_INDUCTION_1_MINTERM)
(|GOOP_INDUCTION_1_MINTERM_GOOP_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|GOOP_INDUCTION_1_MINTERM_pun_def|)
(GOOP_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |GOOP_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |GOOP_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-GOOP_INDUCTION_1_MINTERM)
(NATP_GOOP_INDUCTION_1_MINTERM)
(GOOP_INDUCTION_1_MINTERM_TERM_PROP)
(GOOP_INDUCTION_1_MEASURE)
(GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_1_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_1_MEASURE
 (14 14 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_1_TERMINATES)
(GOOP_INDUCTION_MEASURE)
(GOOP_INDUCTION_TERMINATES)
(GOOP_INDUCTION_TERMINATES_TYPE)
(OPEN_GOOP_INDUCTION_MEASURE
 (36 4 (:REWRITE OPEN_GOOP_INDUCTION_1_TERMINATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_MEASURE!)
(OPEN_GOOP_INDUCTION_TERMINATES
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_X
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES_Y
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_GOOP_INDUCTION_TERMINATES!
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(GOOP_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_GOOP_INDUCTION_REC_TERM
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 )
(GOOP
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_PUN-arity-1-test|)
(|GOOP_PUN-arity-1-base|)
(|GOOP_PUN-arity-1-step|)
(|GOOP_PUN-arity-1-type|)
(|GOOP_PUN-arity-1-stn|)
(|GOOP_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP_PUN-arity-1-stn|))
 )
(|GOOP_PUN-arity-1-CLIQUE|)
(|GOOP_PUN-arity-1-DEF|)
(|GOOP_PUN-arity-1-TYPE|)
(GOOP_PUN)
(GOOP_PUN-DEF
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP_PUN)
(|GOOP-test-1|)
(|GOOP-step-1|)
(|GOOP-inc-1|)
(|GOOP-measure-1|)
(|GOOP-terminates-1|)
(|GOOP-1_PUN-arity-1-test|)
(|GOOP-1_PUN-arity-1-base|)
(|GOOP-1_PUN-arity-1-step|)
(|GOOP-1_PUN-arity-1-type|)
(|GOOP-1_PUN-arity-1-stn|)
(|GOOP-1_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |GOOP-1_PUN-arity-1-stn|))
 )
(|GOOP-1_PUN-arity-1-CLIQUE|)
(|GOOP-1_PUN-arity-1-DEF|)
(|GOOP-1_PUN-arity-1-TYPE|)
(GOOP-1_PUN)
(GOOP-1_PUN-DEF
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN-GOOP-1_PUN)
(GOOP-1
 (22 22 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(GOOP-1_TO_GOOP-1_PUN
 (140 4 (:DEFINITION GOOP-1_PUN-DEF))
 (45 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (19 19 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(|GOOP-1-reduction|
 (70 70 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE DEFAULT-CDR))
 (6 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE DEFAULT-+-1))
 )
(GOOP_PUN_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|GOOP-1-pun-reduction|
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (18 12 (:REWRITE DEFAULT-+-2))
 (18 2 (:DEFINITION GOOP_PUN-DEF))
 (12 12 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:TYPE-PRESCRIPTION GOOP_PUN_INDUCTION))
 )
(|GOOP_to_GOOP_pun|
 (70 2 (:DEFINITION GOOP-1_PUN-DEF))
 (42 6 (:DEFINITION |GOOP-test-1|))
 (40 4 (:REWRITE OPEN_GOOP_INDUCTION_TERMINATES))
 (38 6 (:REWRITE OPEN-GOOP-1_PUN))
 (32 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY))
 (30 30 (:REWRITE DEFAULT-CAR))
 (28 4 (:DEFINITION GOOP_INDUCTIONTEST_BODY_1))
 (22 2 (:DEFINITION |GOOP-inc-1|))
 (15 15 (:REWRITE DEFAULT-CDR))
 (14 2 (:DEFINITION |GOOP-step-1|))
 (8 2 (:DEFINITION INXX))
 (4 4 (:TYPE-PRESCRIPTION GOOP_INDUCTIONTEST_BODY))
 (4 4 (:TYPE-PRESCRIPTION |GOOP-test-1|))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(VFAAT_FN_TEST)
(VFAAT_FN_BASE)
(VFAAT_FN_DEFAULT)
(VFAAT_FN_BRANCH)
(VFAAT_FN_COMP)
(VFAAT_FN_HYP1)
(VFAAT_FN_HYP2)
(VFAAT_FN_TYPE)
(VFAAT_FN_INC)
(VFAAT_FN_INDUCTIONBASE_BODY_1)
(VFAAT_FN_INDUCTIONTEST_BODY_1)
(VFAAT_FN_INDUCTIONTEST_BODY_1_TYPE)
(VFAAT_FN_INDUCTIONSTEP_BODY_1)
(VFAAT_FN_INDUCTIONBASE_BODY)
(VFAAT_FN_INDUCTIONTEST_BODY)
(VFAAT_FN_INDUCTIONSTEP_BODY)
(|VFAAT_FN_INDUCTION_1_MINTERM-pun-stn|)
(|VFAAT_FN_INDUCTION_1_MINTERM-pun-fch-prop|)
(VFAAT_FN_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |VFAAT_FN_INDUCTION_1_MINTERM-pun-stn|))
 )
(VFAAT_FN_INDUCTION_1_MINTERM_TERM_TYPE)
(|VFAAT_FN_INDUCTION_1_MINTERM-xtesq|)
(|VFAAT_FN_INDUCTION_1_MINTERM-xbasq|)
(|VFAAT_FN_INDUCTION_1_MINTERM-xsteq|)
(|VFAAT_FN_INDUCTION_1_MINTERM-xun-stn|)
(|VFAAT_FN_INDUCTION_1_MINTERM-xun-fch-fn|)
(|VFAAT_FN_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FN_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |VFAAT_FN_INDUCTION_1_MINTERM-xun-stn|))
 )
(|VFAAT_FN_INDUCTION_1_MINTERM_pun|)
(VFAAT_FN_INDUCTION_1_MINTERM)
(|VFAAT_FN_INDUCTION_1_MINTERM_VFAAT_FN_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|VFAAT_FN_INDUCTION_1_MINTERM_pun_def|)
(VFAAT_FN_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |VFAAT_FN_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |VFAAT_FN_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-VFAAT_FN_INDUCTION_1_MINTERM)
(NATP_VFAAT_FN_INDUCTION_1_MINTERM)
(VFAAT_FN_INDUCTION_1_MINTERM_TERM_PROP)
(VFAAT_FN_INDUCTION_1_MEASURE)
(VFAAT_FN_INDUCTION_1_TERMINATES)
(VFAAT_FN_INDUCTION_1_TERMINATES_TYPE)
(OPEN_VFAAT_FN_INDUCTION_1_MEASURE
 (14 14 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FN_INDUCTION_1_TERMINATES)
(VFAAT_FN_INDUCTION_MEASURE)
(VFAAT_FN_INDUCTION_TERMINATES)
(VFAAT_FN_INDUCTION_TERMINATES_TYPE)
(OPEN_VFAAT_FN_INDUCTION_MEASURE
 (36 4 (:REWRITE OPEN_VFAAT_FN_INDUCTION_1_TERMINATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FN_INDUCTION_MEASURE!)
(OPEN_VFAAT_FN_INDUCTION_TERMINATES
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FN_INDUCTION_TERMINATES_K
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FN_INDUCTION_TERMINATES_ST
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FN_INDUCTION_TERMINATES!
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FN_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FN_INDUCTION_REC_TERM
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FN
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FN_PUN-arity-1-test|)
(|VFAAT_FN_PUN-arity-1-base|)
(|VFAAT_FN_PUN-arity-1-step|
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FN_INC))
 )
(|VFAAT_FN_PUN-arity-1-type|)
(|VFAAT_FN_PUN-arity-1-stn|)
(|VFAAT_FN_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FN_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |VFAAT_FN_PUN-arity-1-stn|))
 )
(|VFAAT_FN_PUN-arity-1-CLIQUE|)
(|VFAAT_FN_PUN-arity-1-DEF|)
(|VFAAT_FN_PUN-arity-1-TYPE|)
(VFAAT_FN_PUN)
(VFAAT_FN_PUN-DEF
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FN_INC))
 )
(OPEN-VFAAT_FN_PUN)
(VFAAT_FN_STEP_PRESERVES_VFAAT_FN_HYPS)
(VFAAT_FN_TYPE_VFAAT_FN_BASE)
(VFAAT_FN_TYPE_VFAAT_FN_DEFAULT)
(VFAAT_FN_TYPE_VFAAT_FN_INC)
(NATP-VFAAT_FN_INDUCTION_MEASURE)
(VFAAT_FN_INDUCTION_MEASURE_PROPERTY
 (42 42 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(VFAAT_FN_INDUCTION_TERMINATES_PROPERTY
 (12 12 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FN_PUN_PROP
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FN_INC))
 )
(VFAAT_FN_INC_OF-INC
 (12 12 (:TYPE-PRESCRIPTION VFAAT_FN_INC))
 )
(VFAAT_FN_PROPERTY
 (64 10 (:REWRITE OPEN_VFAAT_FN_INDUCTION_TERMINATES))
 (48 6 (:DEFINITION VFAAT_FN_INDUCTIONTEST_BODY))
 (42 6 (:DEFINITION VFAAT_FN_INDUCTIONTEST_BODY_1))
 (30 10 (:REWRITE VFAAT_FN_INDUCTION_TERMINATES_PROPERTY))
 (12 12 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE CAR-CONS))
 (10 10 (:TYPE-PRESCRIPTION VFAAT_FN_HYP2))
 (10 10 (:TYPE-PRESCRIPTION VFAAT_FN_HYP1))
 (6 6 (:TYPE-PRESCRIPTION VFAAT_FN_INDUCTIONTEST_BODY))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CDR-CONS))
 (4 4 (:TYPE-PRESCRIPTION VFAAT_FN_INC))
 )
(VFAAT_FN_TO_FN_PUN
 (78 78 (:REWRITE DEFAULT-CAR))
 (36 36 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FNX_TEST)
(VFAAT_FNX_R0)
(VFAAT_FNX_DEFAULT)
(VFAAT_FNX_BRANCH)
(VFAAT_FNX_COMP)
(VFAAT_FNX_BASE)
(VFAAT_FNX_HYP1)
(VFAAT_FNX_HYP2)
(VFAAT_FNX_TYPE)
(VFAAT_FNX_INC)
(VFAAT_FNX_INDUCTIONBASE_BODY_1)
(VFAAT_FNX_INDUCTIONTEST_BODY_1)
(VFAAT_FNX_INDUCTIONTEST_BODY_1_TYPE)
(VFAAT_FNX_INDUCTIONSTEP_BODY_1)
(VFAAT_FNX_INDUCTIONBASE_BODY)
(VFAAT_FNX_INDUCTIONTEST_BODY)
(VFAAT_FNX_INDUCTIONSTEP_BODY)
(|VFAAT_FNX_INDUCTION_1_MINTERM-pun-stn|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-pun-fch-prop|)
(VFAAT_FNX_INDUCTION_1_MINTERM_TERM
 (3 3 (:TYPE-PRESCRIPTION |VFAAT_FNX_INDUCTION_1_MINTERM-pun-stn|))
 )
(VFAAT_FNX_INDUCTION_1_MINTERM_TERM_TYPE)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xtesq|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xbasq|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xsteq|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xun-stn|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xun-fch-fn|)
(|VFAAT_FNX_INDUCTION_1_MINTERM-xun-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FNX_INDUCTION_1_MINTERM-xun|
 (1 1 (:TYPE-PRESCRIPTION |VFAAT_FNX_INDUCTION_1_MINTERM-xun-stn|))
 )
(|VFAAT_FNX_INDUCTION_1_MINTERM_pun|)
(VFAAT_FNX_INDUCTION_1_MINTERM)
(|VFAAT_FNX_INDUCTION_1_MINTERM_VFAAT_FNX_INDUCTION_1_MINTERM_pun_reduction|
 (102 96 (:REWRITE DEFAULT-CAR))
 (101 38 (:REWRITE ZP-OPEN))
 (91 91 (:REWRITE DEFAULT-+-2))
 (91 91 (:REWRITE DEFAULT-+-1))
 (69 69 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (47 45 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE CAR-CONS))
 (28 28 (:REWRITE CDR-CONS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(|VFAAT_FNX_INDUCTION_1_MINTERM_pun_def|)
(VFAAT_FNX_INDUCTION_1_MINTERM_PROP
 (14 2 (:DEFINITION |VFAAT_FNX_INDUCTION_1_MINTERM-pun-stn|))
 (8 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |VFAAT_FNX_INDUCTION_1_MINTERM-pun-fch-prop|))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:DEFINITION NOT))
 )
(OPEN-VFAAT_FNX_INDUCTION_1_MINTERM)
(NATP_VFAAT_FNX_INDUCTION_1_MINTERM)
(VFAAT_FNX_INDUCTION_1_MINTERM_TERM_PROP)
(VFAAT_FNX_INDUCTION_1_MEASURE)
(VFAAT_FNX_INDUCTION_1_TERMINATES)
(VFAAT_FNX_INDUCTION_1_TERMINATES_TYPE)
(OPEN_VFAAT_FNX_INDUCTION_1_MEASURE
 (14 14 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FNX_INDUCTION_1_TERMINATES)
(VFAAT_FNX_INDUCTION_MEASURE)
(VFAAT_FNX_INDUCTION_TERMINATES)
(VFAAT_FNX_INDUCTION_TERMINATES_TYPE)
(OPEN_VFAAT_FNX_INDUCTION_MEASURE
 (36 4 (:REWRITE OPEN_VFAAT_FNX_INDUCTION_1_TERMINATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FNX_INDUCTION_MEASURE!)
(OPEN_VFAAT_FNX_INDUCTION_TERMINATES
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FNX_INDUCTION_TERMINATES_K
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FNX_INDUCTION_TERMINATES_ST
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(OPEN_VFAAT_FNX_INDUCTION_TERMINATES!
 (32 32 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FNX_INDUCTION
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(OPEN_VFAAT_FNX_INDUCTION_REC_TERM
 (20 20 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FNX
 (46 46 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (5 5 (:TYPE-PRESCRIPTION VFAAT_FNX_BASE))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FNX_PUN-arity-1-test|)
(|VFAAT_FNX_PUN-arity-1-base|)
(|VFAAT_FNX_PUN-arity-1-step|
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 )
(|VFAAT_FNX_PUN-arity-1-type|)
(|VFAAT_FNX_PUN-arity-1-stn|)
(|VFAAT_FNX_PUN-arity-1-fn|
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|VFAAT_FNX_PUN-arity-1|
 (1 1 (:TYPE-PRESCRIPTION |VFAAT_FNX_PUN-arity-1-stn|))
 )
(|VFAAT_FNX_PUN-arity-1-CLIQUE|)
(|VFAAT_FNX_PUN-arity-1-DEF|)
(|VFAAT_FNX_PUN-arity-1-TYPE|)
(VFAAT_FNX_PUN)
(VFAAT_FNX_PUN-DEF
 (9 9 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (4 4 (:TYPE-PRESCRIPTION VFAAT_FNX_BASE))
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 )
(OPEN-VFAAT_FNX_PUN)
(VFAAT_FNX_STEP_PRESERVES_VFAAT_FNX_HYPS)
(VFAAT_FNX_TYPE_VFAAT_FNX_BASE)
(VFAAT_FNX_BASE_VFAAT_FNX_INC_COMMUTE
 (9 6 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 (9 6 (:TYPE-PRESCRIPTION VFAAT_FNX_BASE))
 )
(VFAAT_FNX_TYPE_VFAAT_FNX_R0)
(VFAAT_FNX_TYPE_VFAAT_FNX_DEFAULT)
(VFAAT_FNX_TYPE_VFAAT_FNX_INC)
(NATP-VFAAT_FNX_INDUCTION_MEASURE)
(VFAAT_FNX_INDUCTION_MEASURE_PROPERTY
 (42 42 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(VFAAT_FNX_INDUCTION_TERMINATES_PROPERTY
 (12 12 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(VFAAT_FNX_PUN_PROP
 (4 4 (:TYPE-PRESCRIPTION VFAAT_FNX_BASE))
 (1 1 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 )
(VFAAT_FNX_INC_OF-INC
 (12 12 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 )
(VFAAT_FNX_PROPERTY
 (64 10 (:REWRITE OPEN_VFAAT_FNX_INDUCTION_TERMINATES))
 (48 6 (:DEFINITION VFAAT_FNX_INDUCTIONTEST_BODY))
 (42 6 (:DEFINITION VFAAT_FNX_INDUCTIONTEST_BODY_1))
 (30 10 (:REWRITE VFAAT_FNX_INDUCTION_TERMINATES_PROPERTY))
 (12 12 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE CAR-CONS))
 (10 10 (:TYPE-PRESCRIPTION VFAAT_FNX_HYP2))
 (10 10 (:TYPE-PRESCRIPTION VFAAT_FNX_HYP1))
 (6 6 (:TYPE-PRESCRIPTION VFAAT_FNX_INDUCTIONTEST_BODY))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE CDR-CONS))
 (4 4 (:TYPE-PRESCRIPTION VFAAT_FNX_INC))
 (4 4 (:TYPE-PRESCRIPTION VFAAT_FNX_BASE))
 )
(VFAAT_FNX_TO_FN_PUN
 (90 90 (:REWRITE DEFAULT-CAR))
 (42 42 (:REWRITE DEFAULT-CDR))
 )
