%   ORIGINAL: h4/toto/cpn__distinct_c2
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/toto/GREATER__def: h4/toto/GREATER = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/toto/EQUAL__def: h4/toto/EQUAL = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/toto/datatype__cpn: !cpn. h4/bool/DATATYPE (cpn h4/toto/LESS h4/toto/EQUAL h4/toto/GREATER)
% Assm: h4/toto/cpn2num__thm_c2: h4/toto/cpn2num h4/toto/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/toto/cpn2num__thm_c1: h4/toto/cpn2num h4/toto/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/toto/cpn2num__thm_c0: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm: h4/toto/cpn__EQ__cpn: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/toto/cpn2num__num2cpn: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/toto/cpn2num (h4/toto/num2cpn r) = r
% Assm: h4/toto/cpn__distinct_c1: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm: h4/toto/cpn__distinct_c0: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm: h4/toto/num2cpn__thm_c1: h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/toto/EQUAL
% Assm: h4/toto/cpn__case__def_c1: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm: h4/toto/cpn__case__def_c2: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm: h4/toto/num2cpn__thm_c2: h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/toto/GREATER
% Assm: h4/toto/cpn__CASE0: !x v2 v1 v0. h4/toto/cpn__CASE x v0 v1 v2 = (\m. h4/bool/COND (h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v0 (h4/bool/COND (m = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) v1 v2)) (h4/toto/cpn2num x)
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c6: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/toto/cpn__BIJ_c1: !r. (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) r <=> h4/toto/cpn2num (h4/toto/num2cpn r) = r
% Assm: h4/toto/cpn__BIJ_c0: !a. h4/toto/num2cpn (h4/toto/cpn2num a) = a
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/toto/LESS__def: h4/toto/LESS = h4/toto/num2cpn h4/num/0
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numeral/numeral__eq_c5: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm: h4/numeral/numeral__distrib_c19: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm: h4/toto/cpn__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) rep
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/toto/cpn2num__11: !a_27 a. h4/toto/cpn2num a = h4/toto/cpn2num a_27 <=> a = a_27
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/toto/num2cpn__11: !r_27 r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> h4/prim__rec/_3C r_27 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> (h4/toto/num2cpn r = h4/toto/num2cpn r_27 <=> r = r_27)
% Assm: h4/toto/num2cpn__cpn2num: !a. h4/toto/num2cpn (h4/toto/cpn2num a) = a
% Assm: h4/toto/cpn__case__def_c0: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/LESS v0 v1 v2 = v0
% Assm: h4/toto/num2cpn__thm_c0: h4/toto/num2cpn h4/num/0 = h4/toto/LESS
% Assm: h4/toto/cpn__size__def: !x. h4/toto/cpn__size x = h4/num/0
% Assm: h4/toto/cpn2num__ONTO: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/toto/cpn2num a)
% Assm: h4/toto/num2cpn__ONTO: !a. ?r. a = h4/toto/num2cpn r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/option/IF__EQUALS__OPTION_c0: !x P. h4/bool/COND P (h4/option/SOME x) h4/option/NONE = h4/option/NONE <=> ~P
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/relation/RDOM__DELETE__DEF: !x v u R. h4/relation/RDOM__DELETE R x u v <=> R u v /\ ~(u = x)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/option/NOT__NONE__SOME: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/relation/IN__RDOM__DELETE: !x k R. h4/bool/IN x (h4/relation/RDOM (h4/relation/RDOM__DELETE R k)) <=> h4/bool/IN x (h4/relation/RDOM R) /\ ~(x = k)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sum/sum__distinct: !y x. ~(h4/sum/INL x = h4/sum/INR y)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sum/sum__distinct1: !y x. ~(h4/sum/INR y = h4/sum/INL x)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/IN__DEF: h4/bool/IN = (\x f. f x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/relation/RDOM__DEF: !x R. h4/relation/RDOM R x <=> (?y. R x y)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/pred__set/NOT__SING__EMPTY: !x. ~(h4/pred__set/INSERT x h4/pred__set/EMPTY = h4/pred__set/EMPTY)
% Assm: h4/pred__set/SUBSET__DELETE: !x t s. h4/pred__set/SUBSET s (h4/pred__set/DELETE t x) <=> ~h4/bool/IN x s /\ h4/pred__set/SUBSET s t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/pred__set/IN__SING: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/pred__set/EXTENSION: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm: h4/pred__set/IN__DELETE: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm: h4/pred__set/SUBSET__DEF: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/COND__EXPAND: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/list/LIST__NOT__EQ: !l2 l1. ~(l1 = l2) ==> (!h1 h2. ~(h4/list/CONS h1 l1 = h4/list/CONS h2 l2))
% Assm: h4/bool/COND__DEF: h4/bool/COND = (\t t1 t2. h4/min/_40 (\x. ((t <=> T) ==> x = t1) /\ ((t <=> F) ==> x = t2)))
% Assm: h4/bool/OR__DEF: $or = (\t1 t2. !t. (t1 ==> t) ==> (t2 ==> t) ==> t)
% Assm: h4/bool/F__DEF: F <=> (!t. t)
% Assm: h4/bool/T__DEF: T <=> (\x. x) = (\x. x)
% Assm: h4/bool/NOT__DEF: $not = (\t. t ==> F)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/string/FIELDS__tupled__primitive__def: h4/string/FIELDS__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))))) (\FIELDS__tupled a. h4/pair/pair__CASE a (\P v1. h4/list/list__CASE v1 (h4/combin/I (h4/list/CONS h4/list/NIL h4/list/NIL)) (\h t. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (FIELDS__tupled (h4/pair/_2C P (h4/list/TL r))))))) (h4/rich__list/SPLITP P (h4/list/CONS h t))))))
% Assm: h4/string/TOKENS__tupled__primitive__def: h4/string/TOKENS__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> R (h4/pair/_2C P r) (h4/pair/_2C P (h4/list/CONS h t))))) (\TOKENS__tupled a. h4/pair/pair__CASE a (\P v1. h4/list/list__CASE v1 (h4/combin/I h4/list/NIL) (\h t. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (TOKENS__tupled (h4/pair/_2C P (h4/list/TL r))) (h4/list/CONS l (TOKENS__tupled (h4/pair/_2C P r))))) (h4/rich__list/SPLITP P (h4/list/CONS h t))))))
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/sum/NOT__ISL__ISR: !x. ~h4/sum/ISL x <=> h4/sum/ISR x
% Assm: h4/pred__set/ITSET__IND: !f P. (!s b. (h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> P (h4/pred__set/REST s) (f (h4/pred__set/CHOICE s) b)) ==> P s b) ==> (!v v1. P v v1)
% Assm: h4/sum/ISR0_c1: !y. ~h4/sum/ISR (h4/sum/INL y)
% Assm: h4/sum/ISR0_c0: !x. h4/sum/ISR (h4/sum/INR x)
% Assm: h4/sum/ISL0_c1: !y. ~h4/sum/ISL (h4/sum/INR y)
% Assm: h4/sum/ISL0_c0: !x. h4/sum/ISL (h4/sum/INL x)
% Assm: h4/sum/sum__CASES: !ss. (?x. ss = h4/sum/INL x) \/ (?y. ss = h4/sum/INR y)
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/pred__set/ITSET__curried__def: !x1 x f. h4/pred__set/ITSET f x x1 = h4/pred__set/ITSET__tupled f (h4/pair/_2C x x1)
% Assm: h4/pred__set/CARD__PSUBSET: !s. h4/pred__set/FINITE s ==> (!t. h4/pred__set/PSUBSET t s ==> h4/prim__rec/_3C (h4/pred__set/CARD t) (h4/pred__set/CARD s))
% Assm: h4/pred__set/ITSET__tupled__primitive__def: !f. h4/pred__set/ITSET__tupled f = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> R (h4/pair/_2C (h4/pred__set/REST s) (f (h4/pred__set/CHOICE s) b)) (h4/pair/_2C s b)))) (\ITSET__tupled a. h4/pair/pair__CASE a (\s b. h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND (s = h4/pred__set/EMPTY) b (ITSET__tupled (h4/pair/_2C (h4/pred__set/REST s) (f (h4/pred__set/CHOICE s) b)))) h4/bool/ARB)))
% Assm: h4/pred__set/REST__PSUBSET: !s. ~(s = h4/pred__set/EMPTY) ==> h4/pred__set/PSUBSET (h4/pred__set/REST s) s
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/prim__rec/WF__measure: !m. h4/relation/WF (h4/prim__rec/measure m)
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/prim__rec/measure__def: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Goal: ~(h4/toto/EQUAL = h4/toto/GREATER)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_totos_GREATERu_u_def]: h4/toto/GREATER = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_totos_EQUALu_u_def]: h4/toto/EQUAL = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_totos_datatypeu_u_cpn]: !cpn. h4/bool/DATATYPE (happ (happ (happ cpn h4/toto/LESS) h4/toto/EQUAL) h4/toto/GREATER)
% Assm [h4s_totos_cpn2numu_u_thmu_c2]: h4/toto/cpn2num h4/toto/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_totos_cpn2numu_u_thmu_c1]: h4/toto/cpn2num h4/toto/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/NUMERAL n)) (h4/arithmetic/NUMERAL m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_totos_cpn2numu_u_thmu_c0]: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm [h4s_totos_cpnu_u_EQu_u_cpn]: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_totos_cpn2numu_u_num2cpn]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/toto/cpn2num (h4/toto/num2cpn r) = r
% Assm [h4s_totos_cpnu_u_distinctu_c1]: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm [h4s_totos_cpnu_u_distinctu_c0]: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm [h4s_totos_num2cpnu_u_thmu_c1]: h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/toto/EQUAL
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c1]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c2]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm [h4s_totos_num2cpnu_u_thmu_c2]: h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/toto/GREATER
% Assm [h4s_totos_cpnu_u_CASE0]: !x v2 v1 v0. ?v. (v <=> h4/toto/cpn2num x = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ h4/toto/cpn__CASE x v0 v1 v2 = h4/bool/COND (happ (happ h4/prim__rec/_3C (h4/toto/cpn2num x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v0 (h4/bool/COND v v1 v2)
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_numerals_numeralu_u_ltu_c6]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT2 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. happ (happ h4/prim__rec/_3C n) h4/arithmetic/ZERO <=> F
% Assm [h4s_totos_cpnu_u_BIJu_c1]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/toto/cpn2num (h4/toto/num2cpn r) = r
% Assm [h4s_totos_cpnu_u_BIJu_c0]: !a. h4/toto/num2cpn (h4/toto/cpn2num a) = a
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_totos_LESSu_u_def]: h4/toto/LESS = h4/toto/num2cpn h4/num/0
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numerals_numeralu_u_equ_c5]: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c19]: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm [h4s_totos_cpnu_u_TYu_u_DEF]: !_0. (!n. happ _0 n <=> happ (happ h4/prim__rec/_3C n) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_totos_cpn2numu_u_11]: !a_27 a. h4/toto/cpn2num a = h4/toto/cpn2num a_27 <=> a = a_27
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_totos_num2cpnu_u_11]: !r_27 r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> happ (happ h4/prim__rec/_3C r_27) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> (h4/toto/num2cpn r = h4/toto/num2cpn r_27 <=> r = r_27)
% Assm [h4s_totos_num2cpnu_u_cpn2num]: !a. h4/toto/num2cpn (h4/toto/cpn2num a) = a
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c0]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/LESS v0 v1 v2 = v0
% Assm [h4s_totos_num2cpnu_u_thmu_c0]: h4/toto/num2cpn h4/num/0 = h4/toto/LESS
% Assm [h4s_totos_cpnu_u_sizeu_u_def]: !x. h4/toto/cpn__size x = h4/num/0
% Assm [h4s_totos_cpn2numu_u_ONTO]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/toto/cpn2num a)
% Assm [h4s_totos_num2cpnu_u_ONTO]: !a. ?r. a = h4/toto/num2cpn r /\ happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c0]: !x P. h4/bool/COND P (h4/option/SOME x) h4/option/NONE = h4/option/NONE <=> ~P
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_relations_RDOMu_u_DELETEu_u_DEF]: !x v u R. happ (happ (h4/relation/RDOM__DELETE R x) u) v <=> happ (happ R u) v /\ ~(u = x)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_options_NOTu_u_NONEu_u_SOME]: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_relations_INu_u_RDOMu_u_DELETE]: !x k R. h4/bool/IN x (h4/relation/RDOM (h4/relation/RDOM__DELETE R k)) <=> h4/bool/IN x (h4/relation/RDOM R) /\ ~(x = k)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sums_sumu_u_distinct]: !y x. ~(h4/sum/INL x = h4/sum/INR y)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sums_sumu_u_distinct1]: !y x. ~(h4/sum/INR y = h4/sum/INL x)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_INu_u_DEF]: !x x. h4/bool/IN x x <=> happ x x
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_relations_RDOMu_u_DEF]: !x R. happ (h4/relation/RDOM R) x <=> (?y. happ (happ R x) y)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_predu_u_sets_NOTu_u_SINGu_u_EMPTY]: !x. ~(h4/pred__set/INSERT x h4/pred__set/EMPTY = h4/pred__set/EMPTY)
% Assm [h4s_predu_u_sets_SUBSETu_u_DELETE]: !x t s. h4/pred__set/SUBSET s (h4/pred__set/DELETE t x) <=> ~h4/bool/IN x s /\ h4/pred__set/SUBSET s t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_predu_u_sets_INu_u_SING]: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_EXTENSION]: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm [h4s_predu_u_sets_INu_u_DELETE]: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm [h4s_predu_u_sets_SUBSETu_u_DEF]: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_CONDu_u_EXPAND]: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_lists_LISTu_u_NOTu_u_EQ]: !l2 l1. ~(l1 = l2) ==> (!h1 h2. ~(h4/list/CONS h1 l1 = h4/list/CONS h2 l2))
% Assm [h4s_bools_CONDu_u_DEF]: !_0. (!x x x' x''. happ (happ (happ (happ _0 x) x) x') x'' <=> ((x <=> T) ==> x'' = x) /\ ((x <=> F) ==> x'' = x')) ==> (!x x x'. h4/bool/COND x x x' = h4/min/_40 (happ (happ (happ _0 x) x) x'))
% Assm [h4s_bools_ORu_u_DEF]: !x x'. $or x x' <=> (!t. (x ==> t) ==> (x' ==> t) ==> t)
% Assm [h4s_bools_Fu_u_DEF]: F <=> (!t. t)
% Assm [h4s_bools_Tu_u_DEF]: T <=> (!x. x <=> x)
% Assm [h4s_bools_NOTu_u_DEF]: !x. $not x <=> x ==> F
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_strings_FIELDSu_u_tupledu_u_primitiveu_u_def]: !_8. (!l FIELDS__tupled P r. happ (happ (happ (happ _8 l) FIELDS__tupled) P) r = h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (happ FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (happ FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))))) ==> (!_7. (!FIELDS__tupled P l. happ (happ (happ _7 FIELDS__tupled) P) l = happ (happ (happ _8 l) FIELDS__tupled) P) ==> (!_6. (!FIELDS__tupled P h t. happ (happ (happ (happ _6 FIELDS__tupled) P) h) t = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ _7 FIELDS__tupled) P)) (h4/rich__list/SPLITP P (h4/list/CONS h t)))) ==> (!_5. (!FIELDS__tupled P h. happ (happ (happ _5 FIELDS__tupled) P) h = happ (happ (happ _6 FIELDS__tupled) P) h) ==> (!_4. (!FIELDS__tupled P v1. happ (happ (happ _4 FIELDS__tupled) P) v1 = h4/list/list__CASE v1 (h4/combin/I (h4/list/CONS h4/list/NIL h4/list/NIL)) (happ (happ _5 FIELDS__tupled) P)) ==> (!_3. (!FIELDS__tupled P. happ (happ _3 FIELDS__tupled) P = happ (happ _4 FIELDS__tupled) P) ==> (!_2. (!FIELDS__tupled a. happ (happ _2 FIELDS__tupled) a = h4/pair/pair__CASE a (happ _3 FIELDS__tupled)) ==> (!_1. (!FIELDS__tupled. happ _1 FIELDS__tupled = happ _2 FIELDS__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t)))) ==> h4/string/FIELDS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_strings_TOKENSu_u_tupledu_u_primitiveu_u_def]: !_8. (!l TOKENS__tupled P r. happ (happ (happ (happ _8 l) TOKENS__tupled) P) r = h4/bool/COND (h4/list/NULL l) (happ TOKENS__tupled (h4/pair/_2C P (h4/list/TL r))) (h4/list/CONS l (happ TOKENS__tupled (h4/pair/_2C P r)))) ==> (!_7. (!TOKENS__tupled P l. happ (happ (happ _7 TOKENS__tupled) P) l = happ (happ (happ _8 l) TOKENS__tupled) P) ==> (!_6. (!TOKENS__tupled P h t. happ (happ (happ (happ _6 TOKENS__tupled) P) h) t = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ _7 TOKENS__tupled) P)) (h4/rich__list/SPLITP P (h4/list/CONS h t)))) ==> (!_5. (!TOKENS__tupled P h. happ (happ (happ _5 TOKENS__tupled) P) h = happ (happ (happ _6 TOKENS__tupled) P) h) ==> (!_4. (!TOKENS__tupled P v1. happ (happ (happ _4 TOKENS__tupled) P) v1 = h4/list/list__CASE v1 (h4/combin/I h4/list/NIL) (happ (happ _5 TOKENS__tupled) P)) ==> (!_3. (!TOKENS__tupled P. happ (happ _3 TOKENS__tupled) P = happ (happ _4 TOKENS__tupled) P) ==> (!_2. (!TOKENS__tupled a. happ (happ _2 TOKENS__tupled) a = h4/pair/pair__CASE a (happ _3 TOKENS__tupled)) ==> (!_1. (!TOKENS__tupled. happ _1 TOKENS__tupled = happ _2 TOKENS__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> happ (happ R (h4/pair/_2C P r)) (h4/pair/_2C P (h4/list/CONS h t)))) ==> h4/string/TOKENS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_sums_NOTu_u_ISLu_u_ISR]: !x. ~h4/sum/ISL x <=> h4/sum/ISR x
% Assm [h4s_predu_u_sets_ITSETu_u_IND]: !f P. (!s b. (h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> happ (happ P (h4/pred__set/REST s)) (happ (happ f (h4/pred__set/CHOICE s)) b)) ==> happ (happ P s) b) ==> (!v v1. happ (happ P v) v1)
% Assm [h4s_sums_ISR0u_c1]: !y. ~h4/sum/ISR (h4/sum/INL y)
% Assm [h4s_sums_ISR0u_c0]: !x. h4/sum/ISR (h4/sum/INR x)
% Assm [h4s_sums_ISL0u_c1]: !y. ~h4/sum/ISL (h4/sum/INR y)
% Assm [h4s_sums_ISL0u_c0]: !x. h4/sum/ISL (h4/sum/INL x)
% Assm [h4s_sums_sumu_u_CASES]: !ss. (?x. ss = h4/sum/INL x) \/ (?y. ss = h4/sum/INR y)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_predu_u_sets_ITSETu_u_curriedu_u_def]: !x1 x f. h4/pred__set/ITSET f x x1 = happ (h4/pred__set/ITSET__tupled f) (h4/pair/_2C x x1)
% Assm [h4s_predu_u_sets_CARDu_u_PSUBSET]: !s. h4/pred__set/FINITE s ==> (!t. h4/pred__set/PSUBSET t s ==> happ (happ h4/prim__rec/_3C (h4/pred__set/CARD t)) (h4/pred__set/CARD s))
% Assm [h4s_predu_u_sets_ITSETu_u_tupledu_u_primitiveu_u_def]: !_4. (!ITSET__tupled f s b. ?v. (v <=> s = h4/pred__set/EMPTY) /\ happ (happ (happ (happ _4 ITSET__tupled) f) s) b = h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND v b (happ ITSET__tupled (h4/pair/_2C (h4/pred__set/REST s) (happ (happ f (h4/pred__set/CHOICE s)) b)))) h4/bool/ARB)) ==> (!_3. (!ITSET__tupled f s. happ (happ (happ _3 ITSET__tupled) f) s = happ (happ (happ _4 ITSET__tupled) f) s) ==> (!_2. (!ITSET__tupled f a. happ (happ (happ _2 ITSET__tupled) f) a = h4/pair/pair__CASE a (happ (happ _3 ITSET__tupled) f)) ==> (!_1. (!f ITSET__tupled. happ (happ _1 f) ITSET__tupled = happ (happ _2 ITSET__tupled) f) ==> (!_0. (!f R. happ (happ _0 f) R <=> h4/relation/WF R /\ (!b s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> happ (happ R (h4/pair/_2C (h4/pred__set/REST s) (happ (happ f (h4/pred__set/CHOICE s)) b))) (h4/pair/_2C s b))) ==> (!f. h4/pred__set/ITSET__tupled f = h4/relation/WFREC (h4/min/_40 (happ _0 f)) (happ _1 f))))))
% Assm [h4s_predu_u_sets_RESTu_u_PSUBSET]: !s. ~(s = h4/pred__set/EMPTY) ==> h4/pred__set/PSUBSET (h4/pred__set/REST s) s
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_primu_u_recs_WFu_u_measure]: !m. h4/relation/WF (happ h4/prim__rec/measure m)
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_primu_u_recs_measureu_u_def]: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (happ (h4/relation/inv__image R) f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Goal: ~(h4/toto/EQUAL = h4/toto/GREATER)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1343283,TV_Q1343279]: ![V_f, V_g]: (![V_x]: s(TV_Q1343279,happ(s(t_fun(TV_Q1343283,TV_Q1343279),V_f),s(TV_Q1343283,V_x))) = s(TV_Q1343279,happ(s(t_fun(TV_Q1343283,TV_Q1343279),V_g),s(TV_Q1343283,V_x))) => s(t_fun(TV_Q1343283,TV_Q1343279),V_f) = s(t_fun(TV_Q1343283,TV_Q1343279),V_g))).
fof(ah4s_totos_GREATERu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_greater) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_totos_EQUALu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_totos_datatypeu_u_cpn, axiom, ![V_cpn]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_h4s_totos_cpn,t_bool),happ(s(t_fun(t_h4s_totos_cpn,t_fun(t_h4s_totos_cpn,t_bool)),happ(s(t_fun(t_h4s_totos_cpn,t_fun(t_h4s_totos_cpn,t_fun(t_h4s_totos_cpn,t_bool))),V_cpn),s(t_h4s_totos_cpn,h4s_totos_less))),s(t_h4s_totos_cpn,h4s_totos_equal))),s(t_h4s_totos_cpn,h4s_totos_greater))))))).
fof(ah4s_totos_cpn2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_greater))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_totos_cpn2numu_u_thmu_c1, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_equal))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_totos_cpn2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_less))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_totos_cpnu_u_EQu_u_cpn, axiom, ![V_au_27, V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,V_au_27) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))) = s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_au_27))))).
fof(ah4s_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_totos_cpn2numu_u_num2cpn, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_totos_cpnu_u_distinctu_c1, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_cpnu_u_distinctu_c0, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_totos_num2cpnu_u_thmu_c1, axiom, s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_totos_cpn,h4s_totos_equal)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_equal),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v1)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_greater),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v2)).
fof(ah4s_totos_num2cpnu_u_thmu_c2, axiom, s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_totos_cpn,h4s_totos_greater)).
fof(ah4s_totos_cpnu_u_CASE0, axiom, ![TV_u_27a]: ![V_x, V_v2, V_v1, V_v0]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))) & s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,V_x),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_x))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(TV_u_27a,V_v0),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))))))).
fof(ah4s_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c6, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_totos_cpnu_u_BIJu_c1, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_totos_cpnu_u_BIJu_c0, axiom, ![V_a]: s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))))) = s(t_h4s_totos_cpn,V_a)).
fof(ah4s_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_totos_LESSu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_numerals_numeralu_u_equ_c5, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c19, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_totos_cpnu_u_TYu_u_DEF, axiom, ![V_uu_0]: (![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_totos_cpn,t_h4s_nums_num),V_rep)))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_totos_cpn2numu_u_11, axiom, ![V_au_27, V_a]: (s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))) = s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_au_27))) <=> s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,V_au_27))).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_totos_num2cpnu_u_11, axiom, ![V_ru_27, V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_ru_27))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) => (s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_r))) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_ru_27))) <=> s(t_h4s_nums_num,V_r) = s(t_h4s_nums_num,V_ru_27))))).
fof(ah4s_totos_num2cpnu_u_cpn2num, axiom, ![V_a]: s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))))) = s(t_h4s_totos_cpn,V_a)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_less),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v0)).
fof(ah4s_totos_num2cpnu_u_thmu_c0, axiom, s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_totos_cpn,h4s_totos_less)).
fof(ah4s_totos_cpnu_u_sizeu_u_def, axiom, ![V_x]: s(t_h4s_nums_num,h4s_totos_cpnu_u_size(s(t_h4s_totos_cpn,V_x))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_totos_cpn2numu_u_ONTO, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_a]: s(t_h4s_nums_num,V_r) = s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))))).
fof(ah4s_totos_num2cpnu_u_ONTO, axiom, ![V_a]: ?[V_r]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_r))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0, axiom, ![TV_u_27a]: ![V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_P),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) <=> ~ (p(s(t_bool,V_P))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_relations_RDOMu_u_DELETEu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_u, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_relations_rdomu_u_delete(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_u))),s(TV_u_27b,V_v)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_u))),s(TV_u_27b,V_v)))) & ~ (s(TV_u_27a,V_u) = s(TV_u_27a,V_x))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_options_NOTu_u_NONEu_u_SOME, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_relations_INu_u_RDOMu_u_DELETE, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_k, V_R]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_relations_rdom(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_relations_rdomu_u_delete(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_k)))))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_relations_rdom(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R)))))) & ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_k))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sums_sumu_u_distinct, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: ~ (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sums_sumu_u_distinct1, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: ~ (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_INu_u_DEF, axiom, ![TV_u_27a]: ![V_x, V_x0]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_x0))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x0),s(TV_u_27a,V_x)))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_relations_RDOMu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),h4s_relations_rdom(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_x)))) <=> ?[V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_predu_u_sets_NOTu_u_SINGu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))).
fof(ah4s_predu_u_sets_SUBSETu_u_DELETE, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_t),s(TV_u_27a,V_x)))))) <=> (~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) & p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_predu_u_sets_INu_u_SING, axiom, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_predu_u_sets_EXTENSION, axiom, ![TV_u_27a]: ![V_t, V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t) <=> ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ah4s_predu_u_sets_INu_u_DELETE, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_y)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y))))).
fof(ah4s_predu_u_sets_SUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONDu_u_EXPAND, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,h4s_bools_cond(s(t_bool,V_b),s(t_bool,V_t1),s(t_bool,V_t2)))) <=> ((~ (p(s(t_bool,V_b))) | p(s(t_bool,V_t1))) & (p(s(t_bool,V_b)) | p(s(t_bool,V_t2)))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_lists_LISTu_u_NOTu_u_EQ, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (~ (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l2)) => ![V_h1, V_h2]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h1),s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h2),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_bools_CONDu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_x0, V_xi_, V_xi_i_]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x))),s(t_bool,V_x0))),s(TV_u_27a,V_xi_))),s(TV_u_27a,V_xi_i_)))) <=> ((s(t_bool,V_x0) = s(t_bool,t) => s(TV_u_27a,V_xi_i_) = s(TV_u_27a,V_x)) & (s(t_bool,V_x0) = s(t_bool,f) => s(TV_u_27a,V_xi_i_) = s(TV_u_27a,V_xi_)))) => ![V_x, V_x0, V_xi_]: s(TV_u_27a,h4s_bools_cond(s(t_bool,V_x),s(TV_u_27a,V_x0),s(TV_u_27a,V_xi_))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x0))),s(t_bool,V_x))),s(TV_u_27a,V_xi_))))))).
fof(ah4s_bools_ORu_u_DEF, axiom, ![V_x, V_xi_]: (p(s(t_bool,d_or(s(t_bool,V_x),s(t_bool,V_xi_)))) <=> ![V_t]: ((p(s(t_bool,V_x)) => p(s(t_bool,V_t))) => ((p(s(t_bool,V_xi_)) => p(s(t_bool,V_t))) => p(s(t_bool,V_t)))))).
fof(ah4s_bools_Fu_u_DEF, axiom, (p(s(t_bool,f)) <=> ![V_t]: p(s(t_bool,V_t)))).
fof(ah4s_bools_Tu_u_DEF, axiom, (p(s(t_bool,t)) <=> ![V_x]: s(t_bool,V_x) = s(t_bool,V_x))).
fof(ah4s_bools_NOTu_u_DEF, axiom, ![V_x]: (p(s(t_bool,d_not(s(t_bool,V_x)))) <=> (p(s(t_bool,V_x)) => p(s(t_bool,f))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_strings_FIELDSu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_l, V_FIELDSu_u_tupled, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))))))) => ![V_uu_7]: (![V_FIELDSu_u_tupled, V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_6]: (![V_FIELDSu_u_tupled, V_P, V_h, V_t]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))),s(t_h4s_lists_list(t_h4s_strings_char),V_t))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) => ![V_uu_5]: (![V_FIELDSu_u_tupled, V_P, V_h]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) => ![V_uu_4]: (![V_FIELDSu_u_tupled, V_P, V_v1]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_v1),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))))),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))) => ![V_uu_3]: (![V_FIELDSu_u_tupled, V_P]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_2]: (![V_FIELDSu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a),s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))))) => ![V_uu_1]: (![V_FIELDSu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) & (![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) & ![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & (~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_fieldsu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1))))))))))))).
fof(ah4s_strings_TOKENSu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_l, V_TOKENSu_u_tupled, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))) => ![V_uu_7]: (![V_TOKENSu_u_tupled, V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_6]: (![V_TOKENSu_u_tupled, V_P, V_h, V_t]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))),s(t_h4s_lists_list(t_h4s_strings_char),V_t))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) => ![V_uu_5]: (![V_TOKENSu_u_tupled, V_P, V_h]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) => ![V_uu_4]: (![V_TOKENSu_u_tupled, V_P, V_v1]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_v1),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))) => ![V_uu_3]: (![V_TOKENSu_u_tupled, V_P]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_2]: (![V_TOKENSu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a),s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))))) => ![V_uu_1]: (![V_TOKENSu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) & (![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) & ![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_r))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_tokensu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1))))))))))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sums_NOTu_u_ISLu_u_ISR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: (~ (p(s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_x))))) <=> p(s(t_bool,h4s_sums_isr(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_x)))))).
fof(ah4s_predu_u_sets_ITSETu_u_IND, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_P]: (![V_s, V_b]: (((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,t_bool)),V_P),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,V_b))))))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,t_bool)),V_P),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_b))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,t_bool)),V_P),s(t_fun(TV_u_27a,t_bool),V_v))),s(TV_u_27b,V_v1)))))).
fof(ah4s_sums_ISR0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_y]: ~ (p(s(t_bool,h4s_sums_isr(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_y)))))))).
fof(ah4s_sums_ISR0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: p(s(t_bool,h4s_sums_isr(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_x))))))).
fof(ah4s_sums_ISL0u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_y]: ~ (p(s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y)))))))).
fof(ah4s_sums_ISL0u_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_x]: p(s(t_bool,h4s_sums_isl(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))))))).
fof(ah4s_sums_sumu_u_CASES, axiom, ![TV_u_27a,TV_u_27b]: ![V_ss]: (?[V_x]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_ss) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))) | ?[V_y]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_ss) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_predu_u_sets_ITSETu_u_curriedu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_x1, V_x, V_f]: s(TV_u_27b,h4s_predu_u_sets_itset(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27b,V_x1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),h4s_predu_u_sets_itsetu_u_tupled(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27b,V_x1)))))).
fof(ah4s_predu_u_sets_CARDu_u_PSUBSET, axiom, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ![V_t]: (p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(TV_u_27a,t_bool),V_t))))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(TV_u_27a,t_bool),V_s))))))))).
fof(ah4s_predu_u_sets_ITSETu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_4]: (![V_ITSETu_u_tupled, V_f, V_s, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) & s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_b))) = s(TV_u_27b,h4s_combins_i(s(TV_u_27b,h4s_bools_cond(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27b,V_b),s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,V_b))))))))),s(TV_u_27b,h4s_bools_arb)))))) => ![V_uu_3]: (![V_ITSETu_u_tupled, V_f, V_s]: s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))) => ![V_uu_2]: (![V_ITSETu_u_tupled, V_f, V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),V_a))) = s(TV_u_27b,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),V_a),s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))) => ![V_uu_1]: (![V_f, V_ITSETu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))) => ![V_uu_0]: (![V_f, V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R)))) & ![V_b, V_s]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,V_b))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27b,V_b))))))))) => ![V_f]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),h4s_predu_u_sets_itsetu_u_tupled(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))))))))).
fof(ah4s_predu_u_sets_RESTu_u_PSUBSET, axiom, ![TV_u_27a]: ![V_s]: (~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) => p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_primu_u_recs_WFu_u_measure, axiom, ![TV_u_27a]: ![V_m]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure),s(t_fun(TV_u_27a,t_h4s_nums_num),V_m))))))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_primu_u_recs_measureu_u_def, axiom, ![TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure) = s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_invu_u_image(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c)))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ch4s_totos_cpnu_u_distinctu_c2, conjecture, ~ (s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_greater))).
