%   ORIGINAL: h4/words/BIT__UPDATE
% 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/words/word__modify__def: !w f. h4/words/word__modify f w = h4/fcp/FCP (\i. f i (h4/fcp/fcp__index w i))
% Assm: h4/fcp/FCP__UPDATE__def: !b a. h4/fcp/_3A_2B a b = (\m. h4/fcp/FCP (\c. h4/bool/COND (a = c) b (h4/fcp/fcp__index m c)))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/fcp/CART__EQ: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index x i = h4/fcp/fcp__index y i)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/fcp/FCP__BETA: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = g i
% Assm: h4/words/bit__field__insert__def: !l h a. h4/words/bit__field__insert h l a = h4/words/word__modify (\i. h4/bool/COND (h4/arithmetic/_3C_3D l i /\ h4/arithmetic/_3C_3D i h) (h4/fcp/fcp__index a (h4/arithmetic/_2D i l)))
% Assm: h4/words/fcp__n2w: !f. h4/fcp/FCP f = h4/words/word__modify (\i b. f i) (h4/words/n2w h4/num/0)
% Assm: h4/words/word__modify__n2w: !n f. h4/words/word__modify f (h4/words/n2w n) = h4/words/n2w (h4/bit/BIT__MODIFY (h4/fcp/dimindex h4/bool/the__value) f n)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/fcp/FCP__APPLY__UPDATE__THM: !w m index_20out_20of_20range b a. h4/fcp/fcp__index (h4/fcp/_3A_2B a w m) b = h4/bool/COND (h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value)) (h4/bool/COND (a = b) w (h4/fcp/fcp__index m b)) (h4/combin/FAIL h4/fcp/fcp__index index_20out_20of_20range (h4/fcp/_3A_2B a w m) b)
% Assm: h4/fcp/fcp__subst__comp: !y x f. h4/fcp/_3A_2B x y (h4/fcp/FCP f) = h4/fcp/FCP (\c. h4/bool/COND (x = c) y (f c))
% Assm: h4/fcp/FCP__UPDATE__COMMUTES: !m d c b a. ~(a = b) ==> h4/fcp/_3A_2B a c (h4/fcp/_3A_2B b d m) = h4/fcp/_3A_2B b d (h4/fcp/_3A_2B a c m)
% Assm: h4/fcp/APPLY__FCP__UPDATE__ID: !m a. h4/fcp/_3A_2B a (h4/fcp/fcp__index m a) m = m
% Assm: h4/fcp/FCP__UPDATE__EQ: !m c b a. h4/fcp/_3A_2B a c (h4/fcp/_3A_2B a b m) = h4/fcp/_3A_2B a c m
% Assm: h4/fcp/FCP__UPDATE__IMP__ID: !v m a. h4/fcp/fcp__index m a = v ==> h4/fcp/_3A_2B a v m = m
% Assm: h4/fcp/FCP__CONS__def: !v h. h4/fcp/FCP__CONS h v = h4/fcp/_3A_2B h4/num/0 h (h4/fcp/FCP (\i. h4/fcp/fcp__index v (h4/prim__rec/PRE i)))
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__ID: !t b. h4/bool/COND b t t = t
% Assm: h4/words/n2w__def: !n. h4/words/n2w n = h4/fcp/FCP (\i. h4/bit/BIT i n)
% Assm: h4/bit/BIT__MODIFY__THM: !x n f a. h4/prim__rec/_3C x n ==> (h4/bit/BIT x (h4/bit/BIT__MODIFY n f a) <=> f x (h4/bit/BIT x a))
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/fcp/FCP__ETA: !g. h4/fcp/FCP (\i. h4/fcp/fcp__index g i) = g
% Assm: h4/combin/FAIL__THM: !y x. h4/combin/FAIL x y = x
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/numeral/bit__initiality: !zf b2f b1f. ?f. f h4/arithmetic/ZERO = zf /\ (!n. f (h4/arithmetic/BIT1 n) = b1f n (f n)) /\ (!n. f (h4/arithmetic/BIT2 n) = b2f n (f n))
% 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/words/word__index__n2w: !n index_20too_20large i. h4/fcp/fcp__index (h4/words/n2w n) i <=> h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/bit/BIT i n) (h4/combin/FAIL h4/fcp/fcp__index index_20too_20large (h4/words/n2w n) i)
% Assm: h4/words/word__rrx__def: !w c. h4/words/word__rrx (h4/pair/_2C c w) = h4/pair/_2C (h4/words/word__lsb w) (h4/fcp/FCP (\i. h4/bool/COND (i = h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) c (h4/fcp/fcp__index (h4/words/word__lsr w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i)))
% Assm: h4/fcp/index__comp: !n f FCP_20out_20of_20bounds. h4/fcp/fcp__index (h4/fcp/FCP f) n = h4/bool/COND (h4/prim__rec/_3C n (h4/fcp/dimindex h4/bool/the__value)) (f n) (h4/combin/FAIL h4/fcp/fcp__index FCP_20out_20of_20bounds (h4/fcp/FCP f) n)
% Assm: h4/words/add__with__carry__def: !y x carry__in. h4/words/add__with__carry (h4/pair/_2C x (h4/pair/_2C y carry__in)) = h4/bool/LET (\unsigned__sum. h4/bool/LET (\result. h4/bool/LET (h4/bool/LET (\carry__out overflow. h4/pair/_2C result (h4/pair/_2C carry__out overflow)) (~(h4/words/w2n result = unsigned__sum))) ((h4/words/word__msb x <=> h4/words/word__msb y) /\ ~(h4/words/word__msb x <=> h4/words/word__msb result))) (h4/words/n2w unsigned__sum)) (h4/arithmetic/_2B (h4/arithmetic/_2B (h4/words/w2n x) (h4/words/w2n y)) (h4/bool/COND carry__in (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/num/0))
% Assm: h4/combin/FAIL__DEF: h4/combin/FAIL = (\x y. x)
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/numeral/iSUB__DEF_c1: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m))) (h4/numeral/iBIT__cases x (h4/numeral/iDUB n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB F n m)))
% Assm: h4/rich__list/BUTLASTN__compute: !n longer_20than_20list l. h4/rich__list/BUTLASTN n l = h4/bool/LET (\m. h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/list/TAKE (h4/arithmetic/_2D m n) l) (h4/combin/FAIL h4/rich__list/BUTLASTN longer_20than_20list n l)) (h4/list/LENGTH l)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/numeral/iSUB__DEF_c2: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m))) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)))
% Assm: h4/numeral__bit/LOG__compute: !n m base_20_3C_202_20or_20n_20_3D_200. h4/logroot/LOG m n = h4/bool/COND (h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) \/ n = h4/num/0) (h4/combin/FAIL h4/logroot/LOG base_20_3C_202_20or_20n_20_3D_200 m n) (h4/bool/COND (h4/prim__rec/_3C n m) h4/num/0 (h4/num/SUC (h4/logroot/LOG m (h4/arithmetic/DIV n m))))
% Assm: h4/bit/SBIT__def: !n b. h4/bit/SBIT b n = h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) h4/num/0
% Assm: h4/string/ORD__CHR__COMPUTE: !n _3E_20255. h4/string/ORD (h4/string/CHR n) = h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))) n (h4/combin/FAIL h4/string/ORD _3E_20255 (h4/string/CHR n))
% Assm: h4/ind__type/NUMSUM0: !x b. h4/ind__type/NUMSUM b x = h4/bool/COND b (h4/num/SUC (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% 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/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/rich__list/LASTN__compute: !n longer_20than_20list l. h4/rich__list/LASTN n l = h4/bool/LET (\m. h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/list/DROP (h4/arithmetic/_2D m n) l) (h4/combin/FAIL h4/rich__list/LASTN longer_20than_20list n l)) (h4/list/LENGTH l)
% Assm: h4/option/IF__EQUALS__OPTION_c3: !y x P. h4/bool/COND P h4/option/NONE (h4/option/SOME x) = h4/option/SOME y <=> ~P /\ x = y
% Assm: h4/words/word__bit__n2w: !n b. h4/words/word__bit b (h4/words/n2w n) <=> h4/arithmetic/_3C_3D b (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ h4/bit/BIT b n
% Assm: h4/words/word__bit0: !w b. h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index w b <=> h4/words/word__bit b w)
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/SUB__LEFT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/option/IF__NONE__EQUALS__OPTION_c3: !x X P. h4/bool/COND P h4/option/NONE X = h4/option/SOME x <=> ~P /\ X = h4/option/SOME x
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/bool/COND__EXPAND__IMP: !t2 t1 b. h4/bool/COND b t1 t2 <=> (b ==> t1) /\ (~b ==> t2)
% Assm: h4/sat/dc__cond: !s r q p. (p <=> h4/bool/COND q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~p)
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/rich__list/BUTLASTN__TAKE: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/rich__list/BUTLASTN n l = h4/list/TAKE (h4/arithmetic/_2D (h4/list/LENGTH l) n) l
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% 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/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/option/IF__NONE__EQUALS__OPTION_c0: !X P. h4/bool/COND P X h4/option/NONE = h4/option/NONE <=> P ==> h4/option/IS__NONE X
% Assm: h4/option/NOT__NONE__SOME: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/logroot/LOG__RWT: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m /\ h4/prim__rec/_3C h4/num/0 n ==> h4/logroot/LOG m n = h4/bool/COND (h4/prim__rec/_3C n m) h4/num/0 (h4/num/SUC (h4/logroot/LOG m (h4/arithmetic/DIV n m)))
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/prim__rec/INV__SUC__EQ: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/string/ORD__CHR__RWT: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) ==> h4/string/ORD (h4/string/CHR r) = r
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% 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/EXCLUDED__MIDDLE0: !t. t \/ ~t
% Assm: h4/bool/T__DEF: T <=> (\x. x) = (\x. x)
% Assm: h4/bool/NOT__DEF: $not = (\t. t ==> F)
% Assm: h4/rich__list/LASTN__DROP: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/rich__list/LASTN n l = h4/list/DROP (h4/arithmetic/_2D (h4/list/LENGTH l) n) l
% Assm: h4/option/SOME__11: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/option/IF__EQUALS__OPTION_c2: !y x P. h4/bool/COND P (h4/option/SOME x) h4/option/NONE = h4/option/SOME y <=> P /\ x = y
% Assm: h4/option/IF__EQUALS__OPTION_c1: !x P. h4/bool/COND P h4/option/NONE (h4/option/SOME x) = h4/option/NONE <=> P
% Assm: h4/option/IS__NONE__DEF_c0: !x. h4/option/IS__NONE (h4/option/SOME x) <=> F
% Assm: h4/option/IS__SOME__DEF_c1: h4/option/IS__SOME h4/option/NONE <=> F
% Assm: h4/option/IS__SOME__DEF_c0: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm: h4/option/IS__NONE__DEF_c1: h4/option/IS__NONE h4/option/NONE <=> T
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% Assm: h4/bool/AND1__THM: !t2 t1. t1 /\ t2 ==> t1
% Goal: !x n. h4/fcp/_3A_2B n x = h4/words/word__modify (\i b. h4/bool/COND (i = n) x b)
%   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_wordss_wordu_u_modifyu_u_def]: !_0. (!f w i. happ (happ (happ _0 f) w) i <=> happ (happ f i) (happ (happ h4/fcp/fcp__index w) i)) ==> (!w f. happ (h4/words/word__modify f) w = h4/fcp/FCP (happ (happ _0 f) w))
% Assm [h4s_fcps_FCPu_u_UPDATEu_u_def]: !_0. (!a b x c. ?v. (v <=> a = c) /\ happ (happ (happ (happ _0 a) b) x) c = happ (h4/bool/COND v b) (happ (happ h4/fcp/fcp__index x) c)) ==> (!b a x. happ (h4/fcp/_3A_2B a b) x = h4/fcp/FCP (happ (happ (happ _0 a) b) x))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_fcps_CARTu_u_EQ]: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> happ (happ h4/fcp/fcp__index x) i = happ (happ h4/fcp/fcp__index y) i)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> happ (happ h4/fcp/fcp__index (h4/fcp/FCP g)) i = happ g i
% Assm [h4s_wordss_bitu_u_fieldu_u_insertu_u_def]: !_0. (!h a l i. ?v. (v <=> h4/arithmetic/_3C_3D l i /\ h4/arithmetic/_3C_3D i h) /\ happ (happ (happ (happ _0 h) a) l) i = h4/bool/COND v (happ (happ h4/fcp/fcp__index a) (h4/arithmetic/_2D i l))) ==> (!l h a. h4/words/bit__field__insert h l a = h4/words/word__modify (happ (happ (happ _0 h) a) l))
% Assm [h4s_wordss_fcpu_u_n2w]: !_1. (!f i b. happ (happ (happ _1 f) i) b <=> happ f i) ==> (!_0. (!f i. happ (happ _0 f) i = happ (happ _1 f) i) ==> (!f. h4/fcp/FCP f = happ (h4/words/word__modify (happ _0 f)) (h4/words/n2w h4/num/0)))
% Assm [h4s_wordss_wordu_u_modifyu_u_n2w]: !n f. happ (h4/words/word__modify f) (h4/words/n2w n) = h4/words/n2w (h4/bit/BIT__MODIFY (h4/fcp/dimindex h4/bool/the__value) f n)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> happ (h4/bool/COND P x) y = happ (h4/bool/COND Q x_27) y_27
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_fcps_FCPu_u_APPLYu_u_UPDATEu_u_THM]: !w m index_20out_20of_20range b a. ?v. (v <=> a = b) /\ happ (happ h4/fcp/fcp__index (happ (h4/fcp/_3A_2B a w) m)) b = happ (h4/bool/COND (h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value)) (happ (h4/bool/COND v w) (happ (happ h4/fcp/fcp__index m) b))) (happ (happ (h4/combin/FAIL h4/fcp/fcp__index index_20out_20of_20range) (happ (h4/fcp/_3A_2B a w) m)) b)
% Assm [h4s_fcps_fcpu_u_substu_u_comp]: !_0. (!x y f c. ?v. (v <=> x = c) /\ happ (happ (happ (happ _0 x) y) f) c = happ (h4/bool/COND v y) (happ f c)) ==> (!y x f. happ (h4/fcp/_3A_2B x y) (h4/fcp/FCP f) = h4/fcp/FCP (happ (happ (happ _0 x) y) f))
% Assm [h4s_fcps_FCPu_u_UPDATEu_u_COMMUTES]: !m d c b a. ~(a = b) ==> happ (h4/fcp/_3A_2B a c) (happ (h4/fcp/_3A_2B b d) m) = happ (h4/fcp/_3A_2B b d) (happ (h4/fcp/_3A_2B a c) m)
% Assm [h4s_fcps_APPLYu_u_FCPu_u_UPDATEu_u_ID]: !m a. happ (h4/fcp/_3A_2B a (happ (happ h4/fcp/fcp__index m) a)) m = m
% Assm [h4s_fcps_FCPu_u_UPDATEu_u_EQ]: !m c b a. happ (h4/fcp/_3A_2B a c) (happ (h4/fcp/_3A_2B a b) m) = happ (h4/fcp/_3A_2B a c) m
% Assm [h4s_fcps_FCPu_u_UPDATEu_u_IMPu_u_ID]: !v m a. happ (happ h4/fcp/fcp__index m) a = v ==> happ (h4/fcp/_3A_2B a v) m = m
% Assm [h4s_fcps_FCPu_u_CONSu_u_def]: !_0. (!v i. happ (happ _0 v) i = happ (happ h4/fcp/fcp__index v) (h4/prim__rec/PRE i)) ==> (!v h. h4/fcp/FCP__CONS h v = happ (h4/fcp/_3A_2B h4/num/0 h) (h4/fcp/FCP (happ _0 v)))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. happ (h4/bool/COND F t1) t2 = t2
% Assm [h4s_bools_CONDu_u_ID]: !t b. happ (h4/bool/COND b t) t = t
% Assm [h4s_wordss_n2wu_u_def]: !_0. (!n i. happ (happ _0 n) i <=> h4/bit/BIT i n) ==> (!n. h4/words/n2w n = h4/fcp/FCP (happ _0 n))
% Assm [h4s_bits_BITu_u_MODIFYu_u_THM]: !x n f a. h4/prim__rec/_3C x n ==> (h4/bit/BIT x (h4/bit/BIT__MODIFY n f a) <=> happ (happ f x) (h4/bit/BIT x a))
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. happ (h4/bool/COND F t1) t2 = t2
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. happ (h4/bool/COND T t1) t2 = t1
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. happ (h4/bool/COND T t1) t2 = t1
% Assm [h4s_fcps_FCPu_u_ETA]: !_0. (!g i. happ (happ _0 g) i = happ (happ h4/fcp/fcp__index g) i) ==> (!g. h4/fcp/FCP (happ _0 g) = g)
% Assm [h4s_combins_FAILu_u_THM]: !y x. h4/combin/FAIL x y = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_numerals_bitu_u_initiality]: !zf b2f b1f. ?f. happ f h4/arithmetic/ZERO = zf /\ (!n. happ f (h4/arithmetic/BIT1 n) = happ (happ b1f n) (happ f n)) /\ (!n. happ f (h4/arithmetic/BIT2 n) = happ (happ b2f n) (happ f n))
% 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'. happ (h4/bool/COND x x) x' = h4/min/_40 (happ (happ (happ _0 x) x) x'))
% Assm [h4s_wordss_wordu_u_indexu_u_n2w]: !n index_20too_20large i. happ (happ h4/fcp/fcp__index (h4/words/n2w n)) i <=> happ (h4/bool/COND (h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value)) (h4/bit/BIT i n)) (happ (happ (h4/combin/FAIL h4/fcp/fcp__index index_20too_20large) (h4/words/n2w n)) i)
% Assm [h4s_wordss_wordu_u_rrxu_u_def]: !_0. (!c w i. ?v. (v <=> i = h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (happ (happ (happ _0 c) w) i <=> happ (h4/bool/COND v c) (happ (happ h4/fcp/fcp__index (h4/words/word__lsr w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) i))) ==> (!w c. h4/words/word__rrx (h4/pair/_2C c w) = h4/pair/_2C (h4/words/word__lsb w) (h4/fcp/FCP (happ (happ _0 c) w)))
% Assm [h4s_fcps_indexu_u_comp]: !n f FCP_20out_20of_20bounds. happ (happ h4/fcp/fcp__index (h4/fcp/FCP f)) n = happ (h4/bool/COND (h4/prim__rec/_3C n (h4/fcp/dimindex h4/bool/the__value)) (happ f n)) (happ (happ (h4/combin/FAIL h4/fcp/fcp__index FCP_20out_20of_20bounds) (h4/fcp/FCP f)) n)
% Assm [h4s_wordss_addu_u_withu_u_carryu_u_def]: !_3. (!result carry__out overflow. happ (happ (happ _3 result) carry__out) overflow = h4/pair/_2C result (h4/pair/_2C carry__out overflow)) ==> (!_2. (!result carry__out. happ (happ _2 result) carry__out = happ (happ _3 result) carry__out) ==> (!_1. (!unsigned__sum y x result. ?v. (v <=> (h4/words/word__msb x <=> h4/words/word__msb y) /\ ~(h4/words/word__msb x <=> h4/words/word__msb result)) /\ (?v'. (v' <=> ~(h4/words/w2n result = unsigned__sum)) /\ happ (happ (happ (happ _1 unsigned__sum) y) x) result = h4/bool/LET (h4/bool/LET (happ _2 result) v') v)) ==> (!_0. (!y x unsigned__sum. happ (happ (happ _0 y) x) unsigned__sum = h4/bool/LET (happ (happ (happ _1 unsigned__sum) y) x) (h4/words/n2w unsigned__sum)) ==> (!y x carry__in. h4/words/add__with__carry (h4/pair/_2C x (h4/pair/_2C y carry__in)) = h4/bool/LET (happ (happ _0 y) x) (h4/arithmetic/_2B (h4/arithmetic/_2B (h4/words/w2n x) (h4/words/w2n y)) (happ (h4/bool/COND carry__in (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h4/num/0))))))
% Assm [h4s_combins_FAILu_u_DEF]: !x x. h4/combin/FAIL x x = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_numerals_iSUBu_u_DEFu_c1]: !_2. (!n m. happ (happ _2 n) m = h4/numeral/iDUB (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_0. (!n m. happ (happ _0 n) m = h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = happ (h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _0 n) (happ _1 n))) (h4/numeral/iBIT__cases x (h4/numeral/iDUB n) (happ _1 n) (happ _2 n)))))
% Assm [h4s_richu_u_lists_BUTLASTNu_u_compute]: !_0. (!longer_20than_20list n l m. happ (happ (happ (happ _0 longer_20than_20list) n) l) m = happ (h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/list/TAKE (h4/arithmetic/_2D m n) l)) (happ (happ (h4/combin/FAIL h4/rich__list/BUTLASTN longer_20than_20list) n) l)) ==> (!n longer_20than_20list l. happ (happ h4/rich__list/BUTLASTN n) l = h4/bool/LET (happ (happ (happ _0 longer_20than_20list) n) l) (h4/list/LENGTH l))
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_numerals_iSUBu_u_DEFu_c2]: !_2. (!n m. happ (happ _2 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!_0. (!n m. happ (happ _0 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = happ (h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (happ _0 n) (happ _1 n))) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _1 n) (happ _2 n)))))
% Assm [h4s_numeralu_u_bits_LOGu_u_compute]: !n m base_20_3C_202_20or_20n_20_3D_200. ?v. (v <=> h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) \/ n = h4/num/0) /\ happ (happ h4/logroot/LOG m) n = happ (h4/bool/COND v (happ (happ (h4/combin/FAIL h4/logroot/LOG base_20_3C_202_20or_20n_20_3D_200) m) n)) (happ (h4/bool/COND (h4/prim__rec/_3C n m) h4/num/0) (h4/num/SUC (happ (happ h4/logroot/LOG m) (h4/arithmetic/DIV n m))))
% Assm [h4s_bits_SBITu_u_def]: !n b. h4/bit/SBIT b n = happ (h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)) h4/num/0
% Assm [h4s_strings_ORDu_u_CHRu_u_COMPUTE]: !n _3E_20255. happ h4/string/ORD (h4/string/CHR n) = happ (h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))) n) (happ (h4/combin/FAIL h4/string/ORD _3E_20255) (h4/string/CHR n))
% Assm [h4s_indu_u_types_NUMSUM0]: !x b. h4/ind__type/NUMSUM b x = happ (h4/bool/COND b (h4/num/SUC (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x))) (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c0]: !x P. happ (h4/bool/COND P (h4/option/SOME x)) h4/option/NONE = h4/option/NONE <=> ~P
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_richu_u_lists_LASTNu_u_compute]: !_0. (!longer_20than_20list n l m. happ (happ (happ (happ _0 longer_20than_20list) n) l) m = happ (h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/list/DROP (h4/arithmetic/_2D m n) l)) (happ (happ (h4/combin/FAIL h4/rich__list/LASTN longer_20than_20list) n) l)) ==> (!n longer_20than_20list l. happ (happ h4/rich__list/LASTN n) l = h4/bool/LET (happ (happ (happ _0 longer_20than_20list) n) l) (h4/list/LENGTH l))
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c3]: !y x P. happ (h4/bool/COND P h4/option/NONE) (h4/option/SOME x) = h4/option/SOME y <=> ~P /\ x = y
% Assm [h4s_wordss_wordu_u_bitu_u_n2w]: !n b. h4/words/word__bit b (h4/words/n2w n) <=> h4/arithmetic/_3C_3D b (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ h4/bit/BIT b n
% Assm [h4s_wordss_wordu_u_bit0]: !w b. h4/prim__rec/_3C b (h4/fcp/dimindex h4/bool/the__value) ==> (happ (happ h4/fcp/fcp__index w) b <=> h4/words/word__bit b w)
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c3]: !x X P. happ (h4/bool/COND P h4/option/NONE) X = h4/option/SOME x <=> ~P /\ X = h4/option/SOME x
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_bools_CONDu_u_EXPANDu_u_IMP]: !t2 t1 b. happ (h4/bool/COND b t1) t2 <=> (b ==> t1) /\ (~b ==> t2)
% Assm [h4s_sats_dcu_u_cond]: !s r q p. (p <=> happ (h4/bool/COND q r) s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~p)
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_richu_u_lists_BUTLASTNu_u_TAKE]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> happ (happ h4/rich__list/BUTLASTN n) l = h4/list/TAKE (h4/arithmetic/_2D (h4/list/LENGTH l) n) l
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% 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_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c0]: !X P. happ (h4/bool/COND P X) h4/option/NONE = h4/option/NONE <=> P ==> h4/option/IS__NONE X
% Assm [h4s_options_NOTu_u_NONEu_u_SOME]: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm [h4s_logroots_LOGu_u_RWT]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m /\ h4/prim__rec/_3C h4/num/0 n ==> happ (happ h4/logroot/LOG m) n = happ (h4/bool/COND (h4/prim__rec/_3C n m) h4/num/0) (h4/num/SUC (happ (happ h4/logroot/LOG m) (h4/arithmetic/DIV n m)))
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_primu_u_recs_INVu_u_SUCu_u_EQ]: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_strings_ORDu_u_CHRu_u_RWT]: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))) ==> happ h4/string/ORD (h4/string/CHR r) = r
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% 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_EXCLUDEDu_u_MIDDLE0]: !t. 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_richu_u_lists_LASTNu_u_DROP]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> happ (happ h4/rich__list/LASTN n) l = h4/list/DROP (h4/arithmetic/_2D (h4/list/LENGTH l) n) l
% Assm [h4s_options_SOMEu_u_11]: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c2]: !y x P. happ (h4/bool/COND P (h4/option/SOME x)) h4/option/NONE = h4/option/SOME y <=> P /\ x = y
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c1]: !x P. happ (h4/bool/COND P h4/option/NONE) (h4/option/SOME x) = h4/option/NONE <=> P
% Assm [h4s_options_ISu_u_NONEu_u_DEFu_c0]: !x. h4/option/IS__NONE (h4/option/SOME x) <=> F
% Assm [h4s_options_ISu_u_SOMEu_u_DEFu_c1]: h4/option/IS__SOME h4/option/NONE <=> F
% Assm [h4s_options_ISu_u_SOMEu_u_DEFu_c0]: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm [h4s_options_ISu_u_NONEu_u_DEFu_c1]: h4/option/IS__NONE h4/option/NONE <=> T
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% Assm [h4s_bools_AND1u_u_THM]: !t2 t1. t1 /\ t2 ==> t1
% Goal: !_1. (!i n x b. ?v. (v <=> i = n) /\ (happ (happ (happ (happ _1 i) n) x) b <=> happ (h4/bool/COND v x) b)) ==> (!_0. (!n x i. happ (happ (happ _0 n) x) i = happ (happ (happ _1 i) n) x) ==> (!x n. h4/fcp/_3A_2B n x = h4/words/word__modify (happ (happ _0 n) x)))
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_Q1204379,TV_Q1204375]: ![V_f, V_g]: (![V_x]: s(TV_Q1204375,happ(s(t_fun(TV_Q1204379,TV_Q1204375),V_f),s(TV_Q1204379,V_x))) = s(TV_Q1204375,happ(s(t_fun(TV_Q1204379,TV_Q1204375),V_g),s(TV_Q1204379,V_x))) => s(t_fun(TV_Q1204379,TV_Q1204375),V_f) = s(t_fun(TV_Q1204379,TV_Q1204375),V_g))).
fof(ah4s_wordss_wordu_u_modifyu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_f, V_w, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_i))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))))) => ![V_w, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_fcps_FCPu_u_UPDATEu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_a, V_b, V_x, V_c]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_a) = s(t_h4s_nums_num,V_c)) & s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_a))),s(TV_u_27a,V_b))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_nums_num,V_c))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_b))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_nums_num,V_c)))))) => ![V_b, V_a, V_x]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_b))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_a))),s(TV_u_27a,V_b))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_fcps_CARTu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: (s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y) <=> ![V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y))),s(t_h4s_nums_num,V_i)))))).
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_fcps_FCPu_u_BETA, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_g]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g))))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_i))))).
fof(ah4s_wordss_bitu_u_fieldu_u_insertu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_h, V_a, V_l, V_i]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_i)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_h)))))) & s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))))),V_uu_0),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_a))),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_i))) = s(t_fun(t_bool,t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_a))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_l)))))))) => ![V_l, V_h, V_a]: s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_bitu_u_fieldu_u_insert(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_a))) = s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))))),V_uu_0),s(t_h4s_nums_num,V_h))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_a))),s(t_h4s_nums_num,V_l))))))).
fof(ah4s_wordss_fcpu_u_n2w, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_f, V_i, V_b]: s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_f))),s(t_h4s_nums_num,V_i))),s(t_bool,V_b))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_f),s(t_h4s_nums_num,V_i))) => ![V_uu_0]: (![V_f, V_i]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_f))),s(t_h4s_nums_num,V_i))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_f))),s(t_h4s_nums_num,V_i))) => ![V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),V_f))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_f))))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_wordss_wordu_u_modifyu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_f]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bits_bitu_u_modify(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27))),s(TV_u_27a,V_yu_27))))).
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_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_fcps_FCPu_u_APPLYu_u_UPDATEu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_w, V_m, V_indexu_20outu_20ofu_20range, V_b, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_a) = s(t_h4s_nums_num,V_b)) & s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_w))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))))),s(t_h4s_nums_num,V_b))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_w))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))),s(t_h4s_nums_num,V_b))))))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_bool,V_indexu_20outu_20ofu_20range))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_w))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))))),s(t_h4s_nums_num,V_b))))))).
fof(ah4s_fcps_fcpu_u_substu_u_comp, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_x, V_y, V_f, V_c]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,V_c)) & s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_x))),s(TV_u_27a,V_y))),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,V_c))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_y))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_c)))))) => ![V_y, V_x, V_f]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_x),s(TV_u_27a,V_y))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_x))),s(TV_u_27a,V_y))),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))))))).
fof(ah4s_fcps_FCPu_u_UPDATEu_u_COMMUTES, axiom, ![TV_u_27a,TV_u_27b]: ![V_m, V_d, V_c, V_b, V_a]: (~ (s(t_h4s_nums_num,V_a) = s(t_h4s_nums_num,V_b)) => s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_c))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_b),s(TV_u_27a,V_d))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_b),s(TV_u_27a,V_d))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_c))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))))))).
fof(ah4s_fcps_APPLYu_u_FCPu_u_UPDATEu_u_ID, axiom, ![TV_u_27a,TV_u_27b]: ![V_m, V_a]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))),s(t_h4s_nums_num,V_a))))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m)).
fof(ah4s_fcps_FCPu_u_UPDATEu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_m, V_c, V_b, V_a]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_c))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_b))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_c))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m)))).
fof(ah4s_fcps_FCPu_u_UPDATEu_u_IMPu_u_ID, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_m, V_a]: (s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))),s(t_h4s_nums_num,V_a))) = s(TV_u_27a,V_v) => s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_a),s(TV_u_27a,V_v))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_m))).
fof(ah4s_fcps_FCPu_u_CONSu_u_def, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_v, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_v))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_v))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_i))))) => ![V_v, V_h]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27c),h4s_fcps_fcpu_u_cons(s(TV_u_27a,V_h),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_v))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27c),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27c),t_h4s_fcps_cart(TV_u_27a,TV_u_27c)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_h))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27c),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_v))))))))).
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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,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_bools_CONDu_u_ID, axiom, ![TV_u_27a]: ![V_t, V_b]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_t))),s(TV_u_27a,V_t))) = s(TV_u_27a,V_t)).
fof(ah4s_wordss_n2wu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n, V_i]: 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)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))) => ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(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)),V_uu_0),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bits_BITu_u_MODIFYu_u_THM, axiom, ![V_x, V_n, V_f, V_a]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n)))) => s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_bits_bitu_u_modify(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_a))))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),V_f),s(t_h4s_nums_num,V_x))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_a))))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,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_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,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_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,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_fcps_FCPu_u_ETA, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_g, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_nums_num,V_i))) => ![V_g]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),V_uu_0),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_g))).
fof(ah4s_combins_FAILu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_combins_fail(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
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,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_numerals_bitu_u_initiality, axiom, ![TV_u_27a]: ![V_zf, V_b2f, V_b1f]: ?[V_f]: (s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(TV_u_27a,V_zf) & (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_b1f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))))) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_b2f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))))))).
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,happ(s(t_fun(TV_u_27a,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_wordss_wordu_u_indexu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_indexu_20toou_20large, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_i))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_i),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_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_bool,V_indexu_20toou_20large))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_i)))))).
fof(ah4s_wordss_wordu_u_rrxu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_c, V_w, V_i]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_bool,V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_bool,V_c))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),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_nums_num,V_i)))))) => ![V_w, V_c]: s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_rrx(s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,V_c),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,h4s_wordss_wordu_u_lsb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_bool,V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))))).
fof(ah4s_fcps_indexu_u_comp, axiom, ![TV_u_27b,TV_u_27a]: ![V_n, V_f, V_FCPu_20outu_20ofu_20bounds]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))))),s(t_h4s_nums_num,V_n))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n))))),s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_combins_fail(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),t_fun(t_h4s_nums_num,TV_u_27a)),h4s_fcps_fcpu_u_index),s(t_bool,V_FCPu_20outu_20ofu_20bounds))),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_addu_u_withu_u_carryu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_result, V_carryu_u_out, V_overflow]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_3),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))),s(t_bool,V_overflow))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result),s(t_h4s_pairs_prod(t_bool,t_bool),h4s_pairs_u_2c(s(t_bool,V_carryu_u_out),s(t_bool,V_overflow))))) => ![V_uu_2]: (![V_result, V_carryu_u_out]: s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_2),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))) = s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_3),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_carryu_u_out))) => ![V_uu_1]: (![V_unsignedu_u_sum, V_y, V_x, V_result]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))) & ~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result)))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> ~ (s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))) = s(t_h4s_nums_num,V_unsignedu_u_sum))) & s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_1),s(t_h4s_nums_num,V_unsignedu_u_sum))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_bool,t_fun(t_bool,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_2),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_result))),s(t_bool,V_vi_))),s(t_bool,V_v))))) => ![V_uu_0]: (![V_y, V_x, V_unsignedu_u_sum]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,V_unsignedu_u_sum))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_1),s(t_h4s_nums_num,V_unsignedu_u_sum))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_unsignedu_u_sum))))) => ![V_y, V_x, V_carryu_u_in]: s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_wordss_addu_u_withu_u_carry(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_bool)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_bool),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y),s(t_bool,V_carryu_u_in))))))) = s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_bool))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_y))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_carryu_u_in),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_nums_num,h4s_nums_0)))))))))))).
fof(ah4s_combins_FAILu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27a,h4s_combins_fail(s(TV_u_27a,V_x),s(TV_u_27b,V_x0))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_numerals_iSUBu_u_DEFu_c1, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_richu_u_lists_BUTLASTNu_u_compute, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_longeru_20thanu_20list, V_n, V_l, V_m]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_combins_fail(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_butlastn),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))) => ![V_n, V_longeru_20thanu_20list, V_l]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_butlastn),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
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_numerals_iSUBu_u_DEFu_c2, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_numeralu_u_bits_LOGu_u_compute, axiom, ![V_n, V_m, V_baseu_20u_3Cu_202u_20oru_20nu_20u_3Du_200]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),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_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))) & s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_combins_fail(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_bool,V_baseu_20u_3Cu_202u_20oru_20nu_20u_3Du_200))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))))))))).
fof(ah4s_bits_SBITu_u_def, axiom, ![V_n, V_b]: s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,V_b),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_exp(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_nums_num,V_n))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_strings_ORDu_u_CHRu_u_COMPUTE, axiom, ![V_n, V_uu_3Eu_20255]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(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_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(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,V_n))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_combins_fail(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_bool,V_uu_3Eu_20255))),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_indu_u_types_NUMSUM0, axiom, ![V_x, V_b]: s(t_h4s_nums_num,h4s_indu_u_types_numsum(s(t_bool,V_b),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_nums_num,V_x))))))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_nums_num,V_x)))))).
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),happ(s(t_fun(t_h4s_options_option(TV_u_27a),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_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_nums_num,V_n)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_richu_u_lists_LASTNu_u_compute, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_longeru_20thanu_20list, V_n, V_l, V_m]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_combins_fail(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_lastn),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))) => ![V_n, V_longeru_20thanu_20list, V_l]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_lastn),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_bool,V_longeru_20thanu_20list))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c3, axiom, ![TV_u_27a]: ![V_y, V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_options_option(TV_u_27a),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_none))),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_some(s(TV_u_27a,V_y))) <=> (~ (p(s(t_bool,V_P))) & s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_wordss_wordu_u_bitu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_b]: (p(s(t_bool,h4s_wordss_wordu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n)))))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) & p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_wordu_u_bit0, axiom, ![TV_u_27a]: ![V_w, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) => s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),h4s_fcps_fcpu_u_index),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_b))) = s(t_bool,h4s_wordss_wordu_u_bit(s(t_h4s_nums_num,V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c3, axiom, ![TV_u_27a]: ![V_x, V_X, V_P]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_options_option(TV_u_27a),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_none))),s(t_h4s_options_option(TV_u_27a),V_X))) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))) <=> (~ (p(s(t_bool,V_P))) & s(t_h4s_options_option(TV_u_27a),V_X) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x)))))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(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_x)))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_CONDu_u_EXPANDu_u_IMP, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,happ(s(t_fun(t_bool,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_sats_dcu_u_cond, axiom, ![V_s, V_r, V_q, V_p]: (s(t_bool,V_p) = s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_bools_cond(s(t_bool,V_q),s(t_bool,V_r))),s(t_bool,V_s))) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_s))))) & ((p(s(t_bool,V_p)) | (~ (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_s))))) & ((~ (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_s)) | ~ (p(s(t_bool,V_p))))))))))).
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_richu_u_lists_BUTLASTNu_u_TAKE, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_butlastn),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
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_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_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_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_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_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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c0, axiom, ![TV_u_27a]: ![V_X, V_P]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_h4s_options_option(TV_u_27a)),h4s_bools_cond(s(t_bool,V_P),s(t_h4s_options_option(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)) => p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(TV_u_27a),V_X))))))).
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_logroots_LOGu_u_RWT, axiom, ![V_n, V_m]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(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_nums_num,V_m)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))))))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_primu_u_recs_INVu_u_SUCu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
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_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_strings_ORDu_u_CHRu_u_RWT, axiom, ![V_r]: (p(s(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_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(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,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
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_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_EXCLUDEDu_u_MIDDLE0, axiom, ![V_t]: (p(s(t_bool,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_richu_u_lists_LASTNu_u_DROP, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_lastn),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_options_SOMEu_u_11, axiom, ![TV_u_27a]: ![V_y, V_x]: (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_some(s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
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_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_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2, axiom, ![TV_u_27a]: ![V_y, V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_options_option(TV_u_27a),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_some(s(TV_u_27a,V_y))) <=> (p(s(t_bool,V_P)) & s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c1, axiom, ![TV_u_27a]: ![V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_options_option(TV_u_27a),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_none))),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) <=> p(s(t_bool,V_P)))).
fof(ah4s_options_ISu_u_NONEu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(t_bool,f)).
fof(ah4s_options_ISu_u_SOMEu_u_DEFu_c1, axiom, ![TV_u_27a]: s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,f)).
fof(ah4s_options_ISu_u_SOMEu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(t_bool,t)).
fof(ah4s_options_ISu_u_NONEu_u_DEFu_c1, axiom, ![TV_u_27a]: s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,t)).
fof(ah4s_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
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_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_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_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_AND1u_u_THM, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t1)))).
fof(ch4s_wordss_BITu_u_UPDATE, conjecture, ![TV_u_27a]: ![V_uu_1]: (![V_i, V_n, V_x, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,V_n)) & s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),V_uu_1),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_n))),s(t_bool,V_x))),s(t_bool,V_b))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_bool,V_x))),s(t_bool,V_b)))) => ![V_uu_0]: (![V_n, V_x, V_i]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_bool,V_x))),s(t_h4s_nums_num,V_i))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_bool,t_bool)))),V_uu_1),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_n))),s(t_bool,V_x))) => ![V_x, V_n]: s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_fcps_u_3au_2b(s(t_h4s_nums_num,V_n),s(t_bool,V_x))) = s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_modify(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_bool,V_x)))))))).
