%   ORIGINAL: h4/transc/DIFF__LN
% 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/transc/DIFF__LN0: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/lim/diffl h4/transc/ln (h4/realax/inv x) x
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/transc/EXP__LN: !x. h4/transc/exp (h4/transc/ln x) = x <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/transc/LN__EXP: !x. h4/transc/ln (h4/transc/exp x) = x
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/transc/EXP__INJ: !y x. h4/transc/exp x = h4/transc/exp y <=> x = y
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/transc/LN__MUL: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/realax/real__mul x y) = h4/realax/real__add (h4/transc/ln x) (h4/transc/ln y)
% Assm: h4/lim/DIFF__INVERSE__LT: !x l g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/realax/real__lt (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/realax/real__lt (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (f x)
% Assm: h4/transc/LN__INV: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/realax/inv x) = h4/realax/real__neg (h4/transc/ln x)
% Assm: h4/real/REAL__POS__NZ: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> ~(x = h4/real/real__of__num h4/num/0)
% Assm: h4/transc/ln0: !x. h4/transc/ln x = h4/min/_40 (\u. h4/transc/exp u = x)
% Assm: h4/transc/LN__1: h4/transc/ln (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num h4/num/0
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/transc/LN__MONO__LE: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/real/real__lte (h4/transc/ln x) (h4/transc/ln y) <=> h4/real/real__lte x y)
% Assm: h4/lim/DIFF__CONT: !x l f. h4/lim/diffl f l x ==> h4/lim/contl f x
% Assm: h4/transc/EXP__MONO__LE: !y x. h4/real/real__lte (h4/transc/exp x) (h4/transc/exp y) <=> h4/real/real__lte x y
% Assm: h4/real/REAL__10: ~(h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__LE__01: h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/real/REAL__LT__LE: !y x. h4/realax/real__lt x y <=> h4/real/real__lte x y /\ ~(x = y)
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/transc/DIFF__EXP: !x. h4/lim/diffl h4/transc/exp (h4/transc/exp x) x
% Assm: h4/transc/ROOT__LT__LEMMA: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/real/pow (h4/transc/exp (h4/real/_2F (h4/transc/ln x) (h4/real/real__of__num (h4/num/SUC n)))) (h4/num/SUC n) = x
% Assm: h4/transc/LN__POW: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/real/pow x n) = h4/realax/real__mul (h4/real/real__of__num n) (h4/transc/ln x)
% Assm: h4/transc/LN__INJ: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/transc/ln x = h4/transc/ln y <=> x = y)
% Assm: h4/transc/LN__LT__X: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/transc/ln x) x
% Assm: h4/transc/LN__MONO__LT: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (h4/transc/ln x) (h4/transc/ln y) <=> h4/realax/real__lt x y)
% Assm: h4/transc/LN__DIV: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/real/_2F x y) = h4/real/real__sub (h4/transc/ln x) (h4/transc/ln y)
% Assm: h4/transc/ROOT__LN: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/root (h4/num/SUC n) x = h4/transc/exp (h4/real/_2F (h4/transc/ln x) (h4/real/real__of__num (h4/num/SUC n)))
% Assm: h4/transc/LN__POS: !x. h4/real/real__lte (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x ==> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/transc/ln x)
% Assm: h4/real/REAL__LT__01: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/transc/LN__LE: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/transc/ln (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x)) x
% Assm: h4/transc/EXP__MONO__LT: !y x. h4/realax/real__lt (h4/transc/exp x) (h4/transc/exp y) <=> h4/realax/real__lt x y
% Assm: h4/transc/EXP__TOTAL: !y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?x. h4/transc/exp x = y)
% Assm: h4/lim/DIFF__INVERSE: !x l g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (f x)
% Assm: h4/real/REAL__INV__POS: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/inv x)
% Assm: h4/real/real__div: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm: h4/transc/EXP__POS__LT: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/transc/exp x)
% Assm: h4/transc/EXP__N: !x n. h4/transc/exp (h4/realax/real__mul (h4/real/real__of__num n) x) = h4/real/pow (h4/transc/exp x) n
% Assm: h4/transc/EXP__0: h4/transc/exp (h4/real/real__of__num h4/num/0) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/lim/DIFF__INVERSE__OPEN: !x l g f b a. h4/realax/real__lt a x /\ h4/realax/real__lt x b /\ (!z. h4/realax/real__lt a z /\ h4/realax/real__lt z b ==> g (f z) = z /\ h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (f x)
% Assm: h4/lim/DIFF__XM1: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl (\x0. h4/realax/inv x0) (h4/realax/real__neg (h4/real/pow (h4/realax/inv x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) x
% Assm: h4/real/REAL__LET__TRANS: !z y x. h4/real/real__lte x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/real/REAL__MUL__RINV: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul x (h4/realax/inv x) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__RNEG__UNIQ: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> y = h4/realax/real__neg x
% Assm: h4/real/REAL__MUL__LINV: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/realax/inv x) x = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__MUL__ASSOC: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm: h4/real/REAL__MUL__SYM: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm: h4/real/real__sub0: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm: h4/transc/EXP__LE__X: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (h4/transc/exp x)
% Assm: h4/transc/EXP__ADD: !y x. h4/transc/exp (h4/realax/real__add x y) = h4/realax/real__mul (h4/transc/exp x) (h4/transc/exp y)
% Assm: h4/real/REAL__LT__MUL: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y)
% Assm: h4/real/REAL__INJ: !n m. h4/real/real__of__num m = h4/real/real__of__num n <=> m = n
% Assm: h4/real/REAL__MUL__RID: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/real/REAL__LTE__TRANS: !z y x. h4/realax/real__lt x y /\ h4/real/real__lte y z ==> h4/realax/real__lt x z
% Assm: h4/real/REAL__LT__ADDL: !y x. h4/realax/real__lt y (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> 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__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/real/REAL__LT__IMP__LE: !y x. h4/realax/real__lt x y ==> h4/real/real__lte x y
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/real/REAL__LE__TRANS: !z y x. h4/real/real__lte x y /\ h4/real/real__lte y z ==> h4/real/real__lte x z
% Assm: h4/real/REAL__LE__REFL: !x. h4/real/real__lte x x
% Assm: h4/real/REAL__NOT__LE: !y x. ~h4/real/real__lte x y <=> h4/realax/real__lt y x
% Assm: h4/real/REAL__LT__RADD: !z y x. h4/realax/real__lt (h4/realax/real__add x z) (h4/realax/real__add y z) <=> h4/realax/real__lt x y
% Assm: h4/real/REAL__NOT__LT: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y x
% Assm: h4/real/REAL__ADD__LID: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/real/REAL__LT__HALF1: !d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm: h4/real/REAL__LT__HALF2: !d. h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm: h4/lim/INTERVAL__CLEMMA: !x b a. h4/realax/real__lt a x /\ h4/realax/real__lt x b ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/real/real__lte (h4/real/abs (h4/real/real__sub y x)) d ==> h4/realax/real__lt a y /\ h4/realax/real__lt y b))
% Assm: h4/bool/SELECT__UNIQUE: !x P. (!y. P y <=> y = x) ==> h4/min/_40 P = x
% Assm: h4/real/REAL__EQ__RMUL: !z y x. h4/realax/real__mul x z = h4/realax/real__mul y z <=> z = h4/real/real__of__num h4/num/0 \/ x = y
% Assm: h4/transc/root0: !x n. h4/transc/root n x = h4/min/_40 (\u. (h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) u) /\ h4/real/pow u n = x)
% Assm: h4/lim/LIM__TRANSFORM: !x0 l g f. h4/lim/tends__real__real (\x. h4/real/real__sub (f x) (g x)) (h4/real/real__of__num h4/num/0) x0 /\ h4/lim/tends__real__real g l x0 ==> h4/lim/tends__real__real f l x0
% Assm: h4/lim/LIM__INV: !x l f. h4/lim/tends__real__real f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/tends__real__real (\x0. h4/realax/inv (f x0)) (h4/realax/inv l) x
% Assm: h4/lim/LIM: !y0 x0 f. h4/lim/tends__real__real f y0 x0 <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs (h4/real/real__sub x x0)) /\ h4/realax/real__lt (h4/real/abs (h4/real/real__sub x x0)) d ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (f x) y0)) e)))
% Assm: h4/real/ABS__NEG: !x. h4/real/abs (h4/realax/real__neg x) = h4/real/abs x
% Assm: h4/real/ABS__NZ: !x. ~(x = h4/real/real__of__num h4/num/0) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs x)
% Assm: h4/real/REAL__SUB__RZERO: !x. h4/real/real__sub x (h4/real/real__of__num h4/num/0) = x
% Assm: h4/real/ABS__ZERO: !x. h4/real/abs x = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__SUB__0: !y x. h4/real/real__sub x y = h4/real/real__of__num h4/num/0 <=> x = y
% Assm: h4/real/REAL__MUL__LID: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/real/REAL__LT__REFL: !x. ~h4/realax/real__lt x x
% Assm: h4/lim/diffl0: !x l f. h4/lim/diffl f l x <=> h4/lim/tends__real__real (\h. h4/real/_2F (h4/real/real__sub (f (h4/realax/real__add x h)) (f x)) h) l (h4/real/real__of__num h4/num/0)
% Assm: h4/lim/LIM__X: !x0. h4/lim/tends__real__real (\x. x) x0 x0
% Assm: h4/lim/LIM__NEG: !x l f. h4/lim/tends__real__real f l x <=> h4/lim/tends__real__real (\x0. h4/realax/real__neg (f x0)) (h4/realax/real__neg l) x
% Assm: h4/lim/LIM__MUL: !x m l g f. h4/lim/tends__real__real f l x /\ h4/lim/tends__real__real g m x ==> h4/lim/tends__real__real (\x0. h4/realax/real__mul (f x0) (g x0)) (h4/realax/real__mul l m) x
% Assm: h4/real/POW__2: !x. h4/real/pow x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/realax/real__mul x x
% Assm: h4/lim/LIM__CONST: !x k. h4/lim/tends__real__real (\x0. k) k x
% Assm: h4/lim/LIM__ADD: !x m l g f. h4/lim/tends__real__real f l x /\ h4/lim/tends__real__real g m x ==> h4/lim/tends__real__real (\x0. h4/realax/real__add (f x0) (g x0)) (h4/realax/real__add l m) x
% Assm: h4/real/REAL__SUB__RDISTRIB: !z y x. h4/realax/real__mul (h4/real/real__sub x y) z = h4/real/real__sub (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm: h4/real/REAL__SUB__LDISTRIB: !z y x. h4/realax/real__mul x (h4/real/real__sub y z) = h4/real/real__sub (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm: h4/real/REAL__EQ__LMUL: !z y x. h4/realax/real__mul x y = h4/realax/real__mul x z <=> x = h4/real/real__of__num h4/num/0 \/ y = z
% Assm: h4/real/REAL__ADD__SUB: !y x. h4/real/real__sub (h4/realax/real__add x y) x = y
% Assm: h4/real/REAL__NEG__SUB: !y x. h4/realax/real__neg (h4/real/real__sub x y) = h4/real/real__sub y x
% Assm: h4/real/REAL__ENTIRE: !y x. h4/realax/real__mul x y = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0 \/ y = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__NEG__RMUL: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul x (h4/realax/real__neg y)
% Assm: h4/real/REAL__ADD__RID: !x. h4/realax/real__add x (h4/real/real__of__num h4/num/0) = x
% Assm: h4/real/REAL__LNEG__UNIQ: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> x = h4/realax/real__neg y
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/lim/CONT__COMPOSE: !x g f. h4/lim/contl f x /\ h4/lim/contl g (f x) ==> h4/lim/contl (\x0. g (f x0)) x
% Assm: h4/lim/DIFF__CARAT: !x l f. h4/lim/diffl f l x <=> (?g. (!z. h4/real/real__sub (f z) (f x) = h4/realax/real__mul (g z) (h4/real/real__sub z x)) /\ h4/lim/contl g x /\ g x = l)
% Assm: h4/lim/CONTL__LIM: !x f. h4/lim/contl f x <=> h4/lim/tends__real__real f (f x) x
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/lim/CONT__INJ__RANGE: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/real/real__lte (h4/real/abs (h4/real/real__sub y (f x))) e ==> (?z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d /\ f z = y)))
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/real/ABS__0: h4/real/abs (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__INV__MUL: !y x. ~(x = h4/real/real__of__num h4/num/0) /\ ~(y = h4/real/real__of__num h4/num/0) ==> h4/realax/inv (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/inv x) (h4/realax/inv y)
% Assm: h4/lim/CONT__INVERSE: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> h4/lim/contl g (f x)
% Assm: h4/real/REAL__DOWN2: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?z. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z /\ h4/realax/real__lt z x /\ h4/realax/real__lt z y)
% Assm: h4/real/REAL__SUB__LZERO: !x. h4/real/real__sub (h4/real/real__of__num h4/num/0) x = h4/realax/real__neg x
% Assm: h4/real/REAL__DIV__RMUL: !y x. ~(y = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/real/_2F x y) y = x
% Goal: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/lim/diffl h4/transc/ln (h4/realax/inv x) x
%   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_transcs_DIFFu_u_LN0]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/lim/diffl h4/transc/ln (h4/realax/inv x) x
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_transcs_EXPu_u_LN]: !x. happ h4/transc/exp (happ h4/transc/ln x) = x <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_transcs_LNu_u_EXP]: !x. happ h4/transc/ln (happ h4/transc/exp x) = x
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_transcs_EXPu_u_INJ]: !y x. happ h4/transc/exp x = happ h4/transc/exp y <=> x = y
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_transcs_LNu_u_MUL]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> happ h4/transc/ln (h4/realax/real__mul x y) = h4/realax/real__add (happ h4/transc/ln x) (happ h4/transc/ln y)
% Assm [h4s_lims_DIFFu_u_INVERSEu_u_LT]: !x l g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/realax/real__lt (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/realax/real__lt (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (happ f x)
% Assm [h4s_transcs_LNu_u_INV]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> happ h4/transc/ln (h4/realax/inv x) = h4/realax/real__neg (happ h4/transc/ln x)
% Assm [h4s_reals_REALu_u_POSu_u_NZ]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> ~(x = h4/real/real__of__num h4/num/0)
% Assm [h4s_transcs_ln0]: !_0. (!x u. happ (happ _0 x) u <=> happ h4/transc/exp u = x) ==> (!x. happ h4/transc/ln x = h4/min/_40 (happ _0 x))
% Assm [h4s_transcs_LNu_u_1]: happ h4/transc/ln (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num h4/num/0
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_transcs_LNu_u_MONOu_u_LE]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/real/real__lte (happ h4/transc/ln x) (happ h4/transc/ln y) <=> h4/real/real__lte x y)
% Assm [h4s_lims_DIFFu_u_CONT]: !x l f. h4/lim/diffl f l x ==> h4/lim/contl f x
% Assm [h4s_transcs_EXPu_u_MONOu_u_LE]: !y x. h4/real/real__lte (happ h4/transc/exp x) (happ h4/transc/exp y) <=> h4/real/real__lte x y
% Assm [h4s_reals_REALu_u_10]: ~(h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_LEu_u_01]: h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_reals_REALu_u_LTu_u_LE]: !y x. h4/realax/real__lt x y <=> h4/real/real__lte x y /\ ~(x = y)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_transcs_DIFFu_u_EXP]: !x. h4/lim/diffl h4/transc/exp (happ h4/transc/exp x) x
% Assm [h4s_transcs_ROOTu_u_LTu_u_LEMMA]: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/real/pow (happ h4/transc/exp (h4/real/_2F (happ h4/transc/ln x) (h4/real/real__of__num (h4/num/SUC n)))) (h4/num/SUC n) = x
% Assm [h4s_transcs_LNu_u_POW]: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> happ h4/transc/ln (h4/real/pow x n) = h4/realax/real__mul (h4/real/real__of__num n) (happ h4/transc/ln x)
% Assm [h4s_transcs_LNu_u_INJ]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (happ h4/transc/ln x = happ h4/transc/ln y <=> x = y)
% Assm [h4s_transcs_LNu_u_LTu_u_X]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (happ h4/transc/ln x) x
% Assm [h4s_transcs_LNu_u_MONOu_u_LT]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (happ h4/transc/ln x) (happ h4/transc/ln y) <=> h4/realax/real__lt x y)
% Assm [h4s_transcs_LNu_u_DIV]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> happ h4/transc/ln (h4/real/_2F x y) = h4/real/real__sub (happ h4/transc/ln x) (happ h4/transc/ln y)
% Assm [h4s_transcs_ROOTu_u_LN]: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/root (h4/num/SUC n) x = happ h4/transc/exp (h4/real/_2F (happ h4/transc/ln x) (h4/real/real__of__num (h4/num/SUC n)))
% Assm [h4s_transcs_LNu_u_POS]: !x. h4/real/real__lte (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x ==> h4/real/real__lte (h4/real/real__of__num h4/num/0) (happ h4/transc/ln x)
% Assm [h4s_reals_REALu_u_LTu_u_01]: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_transcs_LNu_u_LE]: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (happ h4/transc/ln (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x)) x
% Assm [h4s_transcs_EXPu_u_MONOu_u_LT]: !y x. h4/realax/real__lt (happ h4/transc/exp x) (happ h4/transc/exp y) <=> h4/realax/real__lt x y
% Assm [h4s_transcs_EXPu_u_TOTAL]: !y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?x. happ h4/transc/exp x = y)
% Assm [h4s_lims_DIFFu_u_INVERSE]: !x l g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (happ f x)
% Assm [h4s_reals_REALu_u_INVu_u_POS]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/inv x)
% Assm [h4s_reals_realu_u_div]: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm [h4s_transcs_EXPu_u_POSu_u_LT]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (happ h4/transc/exp x)
% Assm [h4s_transcs_EXPu_u_N]: !x n. happ h4/transc/exp (h4/realax/real__mul (h4/real/real__of__num n) x) = h4/real/pow (happ h4/transc/exp x) n
% Assm [h4s_transcs_EXPu_u_0]: happ h4/transc/exp (h4/real/real__of__num h4/num/0) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lims_DIFFu_u_INVERSEu_u_OPEN]: !x l g f b a. h4/realax/real__lt a x /\ h4/realax/real__lt x b /\ (!z. h4/realax/real__lt a z /\ h4/realax/real__lt z b ==> happ g (happ f z) = z /\ h4/lim/contl f z) /\ h4/lim/diffl f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl g (h4/realax/inv l) (happ f x)
% Assm [h4s_lims_DIFFu_u_XM1]: !_0. (!x0. happ _0 x0 = h4/realax/inv x0) ==> (!x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/lim/diffl _0 (h4/realax/real__neg (h4/real/pow (h4/realax/inv x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) x)
% Assm [h4s_reals_REALu_u_LETu_u_TRANS]: !z y x. h4/real/real__lte x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_reals_REALu_u_MULu_u_RINV]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul x (h4/realax/inv x) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_RNEGu_u_UNIQ]: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> y = h4/realax/real__neg x
% Assm [h4s_reals_REALu_u_MULu_u_LINV]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/realax/inv x) x = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_MULu_u_ASSOC]: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm [h4s_reals_REALu_u_MULu_u_SYM]: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm [h4s_reals_realu_u_sub0]: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm [h4s_transcs_EXPu_u_LEu_u_X]: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (happ h4/transc/exp x)
% Assm [h4s_transcs_EXPu_u_ADD]: !y x. happ h4/transc/exp (h4/realax/real__add x y) = h4/realax/real__mul (happ h4/transc/exp x) (happ h4/transc/exp y)
% Assm [h4s_reals_REALu_u_LTu_u_MUL]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y)
% Assm [h4s_reals_REALu_u_INJ]: !n m. h4/real/real__of__num m = h4/real/real__of__num n <=> m = n
% Assm [h4s_reals_REALu_u_MULu_u_RID]: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_reals_REALu_u_LTEu_u_TRANS]: !z y x. h4/realax/real__lt x y /\ h4/real/real__lte y z ==> h4/realax/real__lt x z
% Assm [h4s_reals_REALu_u_LTu_u_ADDL]: !y x. h4/realax/real__lt y (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> 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_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_reals_REALu_u_LTu_u_IMPu_u_LE]: !y x. h4/realax/real__lt x y ==> h4/real/real__lte x y
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_reals_REALu_u_LEu_u_TRANS]: !z y x. h4/real/real__lte x y /\ h4/real/real__lte y z ==> h4/real/real__lte x z
% Assm [h4s_reals_REALu_u_LEu_u_REFL]: !x. h4/real/real__lte x x
% Assm [h4s_reals_REALu_u_NOTu_u_LE]: !y x. ~h4/real/real__lte x y <=> h4/realax/real__lt y x
% Assm [h4s_reals_REALu_u_LTu_u_RADD]: !z y x. h4/realax/real__lt (h4/realax/real__add x z) (h4/realax/real__add y z) <=> h4/realax/real__lt x y
% Assm [h4s_reals_REALu_u_NOTu_u_LT]: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y x
% Assm [h4s_reals_REALu_u_ADDu_u_LID]: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_reals_REALu_u_LTu_u_HALF1]: !d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm [h4s_reals_REALu_u_LTu_u_HALF2]: !d. h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm [h4s_lims_INTERVALu_u_CLEMMA]: !x b a. h4/realax/real__lt a x /\ h4/realax/real__lt x b ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/real/real__lte (h4/real/abs (h4/real/real__sub y x)) d ==> h4/realax/real__lt a y /\ h4/realax/real__lt y b))
% Assm [h4s_bools_SELECTu_u_UNIQUE]: !x P. (!y. happ P y <=> y = x) ==> h4/min/_40 P = x
% Assm [h4s_reals_REALu_u_EQu_u_RMUL]: !z y x. h4/realax/real__mul x z = h4/realax/real__mul y z <=> z = h4/real/real__of__num h4/num/0 \/ x = y
% Assm [h4s_transcs_root0]: !_0. (!n x u. happ (happ (happ _0 n) x) u <=> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) u) /\ h4/real/pow u n = x) ==> (!x n. h4/transc/root n x = h4/min/_40 (happ (happ _0 n) x))
% Assm [h4s_lims_LIMu_u_TRANSFORM]: !_0. (!f g x. happ (happ (happ _0 f) g) x = h4/real/real__sub (happ f x) (happ g x)) ==> (!x0 l g f. h4/lim/tends__real__real (happ (happ _0 f) g) (h4/real/real__of__num h4/num/0) x0 /\ h4/lim/tends__real__real g l x0 ==> h4/lim/tends__real__real f l x0)
% Assm [h4s_lims_LIMu_u_INV]: !_0. (!f x0. happ (happ _0 f) x0 = h4/realax/inv (happ f x0)) ==> (!x l f. h4/lim/tends__real__real f l x /\ ~(l = h4/real/real__of__num h4/num/0) ==> h4/lim/tends__real__real (happ _0 f) (h4/realax/inv l) x)
% Assm [h4s_lims_LIM]: !y0 x0 f. h4/lim/tends__real__real f y0 x0 <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs (h4/real/real__sub x x0)) /\ h4/realax/real__lt (h4/real/abs (h4/real/real__sub x x0)) d ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (happ f x) y0)) e)))
% Assm [h4s_reals_ABSu_u_NEG]: !x. h4/real/abs (h4/realax/real__neg x) = h4/real/abs x
% Assm [h4s_reals_ABSu_u_NZ]: !x. ~(x = h4/real/real__of__num h4/num/0) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs x)
% Assm [h4s_reals_REALu_u_SUBu_u_RZERO]: !x. h4/real/real__sub x (h4/real/real__of__num h4/num/0) = x
% Assm [h4s_reals_ABSu_u_ZERO]: !x. h4/real/abs x = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_SUBu_u_0]: !y x. h4/real/real__sub x y = h4/real/real__of__num h4/num/0 <=> x = y
% Assm [h4s_reals_REALu_u_MULu_u_LID]: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_reals_REALu_u_LTu_u_REFL]: !x. ~h4/realax/real__lt x x
% Assm [h4s_lims_diffl0]: !_0. (!f x h. happ (happ (happ _0 f) x) h = h4/real/_2F (h4/real/real__sub (happ f (h4/realax/real__add x h)) (happ f x)) h) ==> (!x l f. h4/lim/diffl f l x <=> h4/lim/tends__real__real (happ (happ _0 f) x) l (h4/real/real__of__num h4/num/0))
% Assm [h4s_lims_LIMu_u_X]: !_0. (!x. happ _0 x = x) ==> (!x0. h4/lim/tends__real__real _0 x0 x0)
% Assm [h4s_lims_LIMu_u_NEG]: !_0. (!f x0. happ (happ _0 f) x0 = h4/realax/real__neg (happ f x0)) ==> (!x l f. h4/lim/tends__real__real f l x <=> h4/lim/tends__real__real (happ _0 f) (h4/realax/real__neg l) x)
% Assm [h4s_lims_LIMu_u_MUL]: !_0. (!f g x0. happ (happ (happ _0 f) g) x0 = h4/realax/real__mul (happ f x0) (happ g x0)) ==> (!x m l g f. h4/lim/tends__real__real f l x /\ h4/lim/tends__real__real g m x ==> h4/lim/tends__real__real (happ (happ _0 f) g) (h4/realax/real__mul l m) x)
% Assm [h4s_reals_POWu_u_2]: !x. h4/real/pow x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/realax/real__mul x x
% Assm [h4s_lims_LIMu_u_CONST]: !_0. (!k x0. happ (happ _0 k) x0 = k) ==> (!x k. h4/lim/tends__real__real (happ _0 k) k x)
% Assm [h4s_lims_LIMu_u_ADD]: !_0. (!f g x0. happ (happ (happ _0 f) g) x0 = h4/realax/real__add (happ f x0) (happ g x0)) ==> (!x m l g f. h4/lim/tends__real__real f l x /\ h4/lim/tends__real__real g m x ==> h4/lim/tends__real__real (happ (happ _0 f) g) (h4/realax/real__add l m) x)
% Assm [h4s_reals_REALu_u_SUBu_u_RDISTRIB]: !z y x. h4/realax/real__mul (h4/real/real__sub x y) z = h4/real/real__sub (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm [h4s_reals_REALu_u_SUBu_u_LDISTRIB]: !z y x. h4/realax/real__mul x (h4/real/real__sub y z) = h4/real/real__sub (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm [h4s_reals_REALu_u_EQu_u_LMUL]: !z y x. h4/realax/real__mul x y = h4/realax/real__mul x z <=> x = h4/real/real__of__num h4/num/0 \/ y = z
% Assm [h4s_reals_REALu_u_ADDu_u_SUB]: !y x. h4/real/real__sub (h4/realax/real__add x y) x = y
% Assm [h4s_reals_REALu_u_NEGu_u_SUB]: !y x. h4/realax/real__neg (h4/real/real__sub x y) = h4/real/real__sub y x
% Assm [h4s_reals_REALu_u_ENTIRE]: !y x. h4/realax/real__mul x y = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0 \/ y = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_NEGu_u_RMUL]: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul x (h4/realax/real__neg y)
% Assm [h4s_reals_REALu_u_ADDu_u_RID]: !x. h4/realax/real__add x (h4/real/real__of__num h4/num/0) = x
% Assm [h4s_reals_REALu_u_LNEGu_u_UNIQ]: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> x = h4/realax/real__neg y
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_lims_CONTu_u_COMPOSE]: !_0. (!g f x0. happ (happ (happ _0 g) f) x0 = happ g (happ f x0)) ==> (!x g f. h4/lim/contl f x /\ h4/lim/contl g (happ f x) ==> h4/lim/contl (happ (happ _0 g) f) x)
% Assm [h4s_lims_DIFFu_u_CARAT]: !x l f. h4/lim/diffl f l x <=> (?g. (!z. h4/real/real__sub (happ f z) (happ f x) = h4/realax/real__mul (happ g z) (h4/real/real__sub z x)) /\ h4/lim/contl g x /\ happ g x = l)
% Assm [h4s_lims_CONTLu_u_LIM]: !x f. h4/lim/contl f x <=> h4/lim/tends__real__real f (happ f x) x
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_lims_CONTu_u_INJu_u_RANGE]: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/real/real__lte (h4/real/abs (h4/real/real__sub y (happ f x))) e ==> (?z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d /\ happ f z = y)))
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_reals_ABSu_u_0]: h4/real/abs (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_INVu_u_MUL]: !y x. ~(x = h4/real/real__of__num h4/num/0) /\ ~(y = h4/real/real__of__num h4/num/0) ==> h4/realax/inv (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/inv x) (h4/realax/inv y)
% Assm [h4s_lims_CONTu_u_INVERSE]: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> h4/lim/contl g (happ f x)
% Assm [h4s_reals_REALu_u_DOWN2]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?z. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z /\ h4/realax/real__lt z x /\ h4/realax/real__lt z y)
% Assm [h4s_reals_REALu_u_SUBu_u_LZERO]: !x. h4/real/real__sub (h4/real/real__of__num h4/num/0) x = h4/realax/real__neg x
% Assm [h4s_reals_REALu_u_DIVu_u_RMUL]: !y x. ~(y = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/real/_2F x y) y = x
% Goal: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/lim/diffl h4/transc/ln (h4/realax/inv x) 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_Q1285858,TV_Q1285854]: ![V_f, V_g]: (![V_x]: s(TV_Q1285854,happ(s(t_fun(TV_Q1285858,TV_Q1285854),V_f),s(TV_Q1285858,V_x))) = s(TV_Q1285854,happ(s(t_fun(TV_Q1285858,TV_Q1285854),V_g),s(TV_Q1285858,V_x))) => s(t_fun(TV_Q1285858,TV_Q1285854),V_f) = s(t_fun(TV_Q1285858,TV_Q1285854),V_g))).
fof(ah4s_transcs_DIFFu_u_LN0, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x)))))).
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_transcs_EXPu_u_LN, axiom, ![V_x]: (s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_transcs_LNu_u_EXP, axiom, ![V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x)).
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_transcs_EXPu_u_INJ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_y))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_transcs_LNu_u_MUL, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_lims_DIFFu_u_INVERSEu_u_LT, axiom, ![V_x, V_l, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & (![V_z]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) & (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ~ (s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_transcs_LNu_u_INV, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_POSu_u_NZ, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => ~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_transcs_ln0, axiom, ![V_uu_0]: (![V_x, V_u]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_u)))) <=> s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_u))) = s(t_h4s_realaxs_real,V_x)) => ![V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_mins_u_40(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),V_uu_0),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_LNu_u_1, axiom, s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
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_transcs_LNu_u_MONOu_u_LE, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_lims_DIFFu_u_CONT, axiom, ![V_x, V_l, V_f]: (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_transcs_EXPu_u_MONOu_u_LE, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_10, axiom, ~ (s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_reals_REALu_u_LEu_u_01, axiom, p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))).
fof(ah4s_reals_REALu_u_LTu_u_LE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) <=> (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & ~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))))).
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_transcs_DIFFu_u_EXP, axiom, ![V_x]: p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_transcs_ROOTu_u_LTu_u_LEMMA, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,V_x))).
fof(ah4s_transcs_LNu_u_POW, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_LNu_u_INJ, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => (s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_y))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_LNu_u_LTu_u_X, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_transcs_LNu_u_MONOu_u_LT, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_transcs_LNu_u_DIV, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_transcs_ROOTu_u_LN, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,h4s_transcs_root(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_transcs_LNu_u_POS, axiom, ![V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_REALu_u_LTu_u_01, axiom, p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))).
fof(ah4s_transcs_LNu_u_LE, axiom, ![V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_transcs_EXPu_u_MONOu_u_LT, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_EXPu_u_TOTAL, axiom, ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y)))) => ?[V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_lims_DIFFu_u_INVERSE, axiom, ![V_x, V_l, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) & (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ~ (s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_REALu_u_INVu_u_POS, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_realu_u_div, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_transcs_EXPu_u_POSu_u_LT, axiom, ![V_x]: p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_EXPu_u_N, axiom, ![V_x, V_n]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_transcs_EXPu_u_0, axiom, s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_bools_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_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_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_lims_DIFFu_u_INVERSEu_u_OPEN, axiom, ![V_x, V_l, V_g, V_f, V_b, V_a]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_a),s(t_h4s_realaxs_real,V_x)))) & (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_b)))) & (![V_z]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_a),s(t_h4s_realaxs_real,V_z)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_b))))) => (s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z) & p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z)))))) & (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ~ (s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_lims_DIFFu_u_XM1, axiom, ![V_uu_0]: (![V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_uu_0),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x0))) => ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_uu_0),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),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_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_LETu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_reals_REALu_u_MULu_u_RINV, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_reals_REALu_u_RNEGu_u_UNIQ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_reals_REALu_u_MULu_u_LINV, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_reals_REALu_u_MULu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z)))).
fof(ah4s_reals_REALu_u_MULu_u_SYM, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_realu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_transcs_EXPu_u_LEu_u_X, axiom, ![V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_transcs_EXPu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_exp),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_LTu_u_MUL, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))))).
fof(ah4s_reals_REALu_u_INJ, axiom, ![V_n, V_m]: (s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_reals_REALu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x)).
fof(ah4s_nums_NOTu_u_SUC, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_reals_REALu_u_LTEu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_LTu_u_ADDL, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))).
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_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_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_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_reals_REALu_u_LTu_u_IMPu_u_LE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (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_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_reals_REALu_u_LEu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_reals_REALu_u_NOTu_u_LE, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_reals_REALu_u_LTu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) <=> p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_reals_REALu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
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_reals_REALu_u_LTu_u_HALF1, axiom, ![V_d]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))).
fof(ah4s_reals_REALu_u_LTu_u_HALF2, axiom, ![V_d]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_d))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))).
fof(ah4s_lims_INTERVALu_u_CLEMMA, axiom, ![V_x, V_b, V_a]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_a),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_b))))) => ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_y]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_a),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_b))))))))).
fof(ah4s_bools_SELECTu_u_UNIQUE, axiom, ![TV_u_27a]: ![V_x, V_P]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y)))) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x)) => s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P))) = s(TV_u_27a,V_x))).
fof(ah4s_reals_REALu_u_EQu_u_RMUL, axiom, ![V_z, V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))) <=> (s(t_h4s_realaxs_real,V_z) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_root0, axiom, ![V_uu_0]: (![V_n, V_x, V_u]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_u)))) <=> ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_u))))) & s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_u),s(t_h4s_nums_num,V_n))) = s(t_h4s_realaxs_real,V_x))) => ![V_x, V_n]: s(t_h4s_realaxs_real,h4s_transcs_root(s(t_h4s_nums_num,V_n),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_mins_u_40(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_lims_LIMu_u_TRANSFORM, axiom, ![V_uu_0]: (![V_f, V_g, V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x))))) => ![V_x0, V_l, V_g, V_f]: ((p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x0)))) & p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x0))))) => p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x0))))))).
fof(ah4s_lims_LIMu_u_INV, axiom, ![V_uu_0]: (![V_f, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ~ (s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_lims_LIM, axiom, ![V_y0, V_x0, V_f]: (p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_y0),s(t_h4s_realaxs_real,V_x0)))) <=> ![V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x0)))))))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x0))))),s(t_h4s_realaxs_real,V_d))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y0))))),s(t_h4s_realaxs_real,V_e))))))))).
fof(ah4s_reals_ABSu_u_NEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_ABSu_u_NZ, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_REALu_u_SUBu_u_RZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_ABSu_u_ZERO, axiom, ![V_x]: (s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_reals_REALu_u_SUBu_u_0, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_reals_REALu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(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_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_LTu_u_REFL, axiom, ![V_x]: ~ (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_lims_diffl0, axiom, ![V_uu_0]: (![V_f, V_x, V_h]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_h))) = s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_h))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_h))) => ![V_x, V_l, V_f]: s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x))) = s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))).
fof(ah4s_lims_LIMu_u_X, axiom, ![V_uu_0]: (![V_x]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_uu_0),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x) => ![V_x0]: p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_uu_0),s(t_h4s_realaxs_real,V_x0),s(t_h4s_realaxs_real,V_x0)))))).
fof(ah4s_lims_LIMu_u_NEG, axiom, ![V_uu_0]: (![V_f, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_l, V_f]: s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x))) = s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_lims_LIMu_u_MUL, axiom, ![V_uu_0]: (![V_f, V_g, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_m, V_l, V_g, V_f]: ((p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_m),s(t_h4s_realaxs_real,V_x))))) => p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_m))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_POWu_u_2, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),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_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_lims_LIMu_u_CONST, axiom, ![V_uu_0]: (![V_k, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_h4s_realaxs_real,V_k))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,V_k) => ![V_x, V_k]: p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_h4s_realaxs_real,V_k))),s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_lims_LIMu_u_ADD, axiom, ![V_uu_0]: (![V_f, V_g, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_m, V_l, V_g, V_f]: ((p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_m),s(t_h4s_realaxs_real,V_x))))) => p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_m))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_SUBu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_SUBu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_EQu_u_LMUL, axiom, ![V_z, V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))) <=> (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,V_z)))).
fof(ah4s_reals_REALu_u_ADDu_u_SUB, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_y)).
fof(ah4s_reals_REALu_u_NEGu_u_SUB, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_ENTIRE, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_reals_REALu_u_NEGu_u_RMUL, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_LNEGu_u_UNIQ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lims_CONTu_u_COMPOSE, axiom, ![V_uu_0]: (![V_g, V_f, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_g, V_f]: ((p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_lims_DIFFu_u_CARAT, axiom, ![V_x, V_l, V_f]: (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) <=> ?[V_g]: (![V_z]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))) & (p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x)))) & s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_l))))).
fof(ah4s_lims_CONTLu_u_LIM, axiom, ![V_x, V_f]: s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))) = s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_lims_CONTu_u_INJu_u_RANGE, axiom, ![V_x, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & ![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))))) => ?[V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) & ![V_y]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))))),s(t_h4s_realaxs_real,V_e)))) => ?[V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) & s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))) = s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_reals_ABSu_u_0, axiom, s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_REALu_u_INVu_u_MUL, axiom, ![V_y, V_x]: ((~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & ~ (s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_lims_CONTu_u_INVERSE, axiom, ![V_x, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & ![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_REALu_u_DOWN2, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => ?[V_z]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_z)))) & (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_y)))))))).
fof(ah4s_reals_REALu_u_SUBu_u_LZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_DIVu_u_RMUL, axiom, ![V_y, V_x]: (~ (s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,V_x))).
fof(ch4s_transcs_DIFFu_u_LN, conjecture, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_ln),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x)))))).
