%   ORIGINAL: h4/measure/FN__MINUS__ADD__LE
% 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/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% 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/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/real/REAL__ADD__SYM: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm: h4/real/REAL__ADD__ASSOC: !z y x. h4/realax/real__add x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__add x y) z
% Assm: h4/real/REAL__ADD__LID: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm: h4/real/REAL__ADD__LINV: !x. h4/realax/real__add (h4/realax/real__neg x) x = h4/real/real__of__num h4/num/0
% 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__lte0: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% 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__ADD__RINV: !x. h4/realax/real__add x (h4/realax/real__neg x) = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__NEG__ADD: !y x. h4/realax/real__neg (h4/realax/real__add x y) = h4/realax/real__add (h4/realax/real__neg x) (h4/realax/real__neg y)
% Assm: h4/real/REAL__MUL__LZERO: !x. h4/realax/real__mul (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__LE__REFL: !x. h4/real/real__lte x x
% Assm: h4/real/REAL__LE__ANTISYM: !y x. h4/real/real__lte x y /\ h4/real/real__lte y x <=> x = y
% Assm: h4/real/REAL__LE__ADD2: !z y x w. h4/real/real__lte w x /\ h4/real/real__lte y z ==> h4/real/real__lte (h4/realax/real__add w y) (h4/realax/real__add x z)
% Assm: h4/real/REAL__LE__NEG: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm: h4/real/REAL__MUL__LNEG: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/real/real__lt: !y x. h4/realax/real__lt x y <=> ~h4/real/real__lte y x
% Assm: h4/real/REAL__LE__LNEG: !y x. h4/real/real__lte (h4/realax/real__neg x) y <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/realax/real__add x y)
% Assm: h4/real/REAL__LE__NEG2: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm: h4/real/REAL__NEG__NEG: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm: h4/real/REAL__LE__RNEG: !y x. h4/real/real__lte x (h4/realax/real__neg y) <=> h4/real/real__lte (h4/realax/real__add x y) (h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__ADD__RDISTRIB: !z y x. h4/realax/real__mul (h4/realax/real__add x y) z = h4/realax/real__add (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm: h4/extreal/extreal__nchotomy: !ee. ee = h4/extreal/NegInf \/ ee = h4/extreal/PosInf \/ (?r. ee = h4/extreal/Normal r)
% Assm: h4/extreal/extreal__of__num__def: !n. h4/extreal/extreal__of__num n = h4/extreal/Normal (h4/real/real__of__num n)
% Assm: h4/extreal/extreal__add__def_c0: !y x. h4/extreal/extreal__add (h4/extreal/Normal x) (h4/extreal/Normal y) = h4/extreal/Normal (h4/realax/real__add x y)
% Assm: h4/extreal/extreal__add__def_c1: !a. h4/extreal/extreal__add h4/extreal/PosInf a = h4/extreal/PosInf
% Assm: h4/extreal/extreal__add__def_c2: h4/extreal/extreal__add h4/extreal/NegInf h4/extreal/PosInf = h4/extreal/PosInf
% Assm: h4/extreal/extreal__add__def_c3: !v2. h4/extreal/extreal__add (h4/extreal/Normal v2) h4/extreal/PosInf = h4/extreal/PosInf
% Assm: h4/extreal/extreal__add__def_c4: h4/extreal/extreal__add h4/extreal/NegInf h4/extreal/NegInf = h4/extreal/NegInf
% Assm: h4/extreal/extreal__add__def_c5: !v5. h4/extreal/extreal__add h4/extreal/NegInf (h4/extreal/Normal v5) = h4/extreal/NegInf
% Assm: h4/extreal/extreal__add__def_c6: !v3. h4/extreal/extreal__add (h4/extreal/Normal v3) h4/extreal/NegInf = h4/extreal/NegInf
% Assm: h4/extreal/extreal__le__def_c0: !y x. h4/extreal/extreal__le (h4/extreal/Normal x) (h4/extreal/Normal y) <=> h4/real/real__lte x y
% Assm: h4/extreal/extreal__le__def_c2: h4/extreal/extreal__le h4/extreal/PosInf h4/extreal/PosInf <=> T
% Assm: h4/extreal/extreal__le__def_c6: !v5. h4/extreal/extreal__le h4/extreal/PosInf (h4/extreal/Normal v5) <=> F
% Assm: h4/extreal/extreal__lt__def: !y x. h4/extreal/extreal__lt x y <=> ~h4/extreal/extreal__le y x
% Assm: h4/extreal/extreal__ainv__def_c0: h4/extreal/extreal__ainv h4/extreal/NegInf = h4/extreal/PosInf
% Assm: h4/extreal/extreal__ainv__def_c1: h4/extreal/extreal__ainv h4/extreal/PosInf = h4/extreal/NegInf
% Assm: h4/extreal/extreal__ainv__def_c2: !x. h4/extreal/extreal__ainv (h4/extreal/Normal x) = h4/extreal/Normal (h4/realax/real__neg x)
% Assm: h4/extreal/extreal__lt__eq: !y x. h4/extreal/extreal__lt (h4/extreal/Normal x) (h4/extreal/Normal y) <=> h4/realax/real__lt x y
% Assm: h4/extreal/le__refl: !x. h4/extreal/extreal__le x x
% Assm: h4/extreal/le__infty_c0: !x. h4/extreal/extreal__le h4/extreal/NegInf x
% Assm: h4/extreal/lt__infty_c0: !y. h4/extreal/extreal__lt h4/extreal/NegInf (h4/extreal/Normal y)
% Assm: h4/extreal/lt__infty_c1: !y. h4/extreal/extreal__lt (h4/extreal/Normal y) h4/extreal/PosInf
% Assm: h4/extreal/lt__infty_c2: h4/extreal/extreal__lt h4/extreal/NegInf h4/extreal/PosInf
% Assm: h4/extreal/lt__infty_c3: !x. ~h4/extreal/extreal__lt x h4/extreal/NegInf
% Assm: h4/extreal/lt__infty_c4: !x. ~h4/extreal/extreal__lt h4/extreal/PosInf x
% Assm: h4/extreal/lt__infty_c5: !x. ~(x = h4/extreal/PosInf) <=> h4/extreal/extreal__lt x h4/extreal/PosInf
% Assm: h4/extreal/lt__infty_c6: !x. ~(x = h4/extreal/NegInf) <=> h4/extreal/extreal__lt h4/extreal/NegInf x
% Assm: h4/extreal/lt__imp__le: !y x. h4/extreal/extreal__lt x y ==> h4/extreal/extreal__le x y
% Assm: h4/extreal/lt__neg: !y x. h4/extreal/extreal__lt (h4/extreal/extreal__ainv x) (h4/extreal/extreal__ainv y) <=> h4/extreal/extreal__lt y x
% Assm: h4/extreal/le__add2: !z y x w. h4/extreal/extreal__le w x /\ h4/extreal/extreal__le y z ==> h4/extreal/extreal__le (h4/extreal/extreal__add w y) (h4/extreal/extreal__add x z)
% Assm: h4/extreal/add__rzero: !x. h4/extreal/extreal__add x (h4/extreal/extreal__of__num h4/num/0) = x
% Assm: h4/extreal/add__lzero: !x. h4/extreal/extreal__add (h4/extreal/extreal__of__num h4/num/0) x = x
% Assm: h4/extreal/neg__0: h4/extreal/extreal__ainv (h4/extreal/extreal__of__num h4/num/0) = h4/extreal/extreal__of__num h4/num/0
% Assm: h4/measure/fn__minus__def: !f. h4/measure/fn__minus f = (\x. h4/bool/COND (h4/extreal/extreal__lt (f x) (h4/extreal/extreal__of__num h4/num/0)) (h4/extreal/extreal__ainv (f x)) (h4/extreal/extreal__of__num h4/num/0))
% Goal: !x g f. h4/extreal/extreal__le (h4/measure/fn__minus (\x0. h4/extreal/extreal__add (f x0) (g x0)) x) (h4/extreal/extreal__add (h4/measure/fn__minus f x) (h4/measure/fn__minus g 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_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% 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_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_reals_REALu_u_ADDu_u_SYM]: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm [h4s_reals_REALu_u_ADDu_u_ASSOC]: !z y x. h4/realax/real__add x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__add x y) z
% 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_reals_REALu_u_ADDu_u_LINV]: !x. h4/realax/real__add (h4/realax/real__neg x) x = h4/real/real__of__num h4/num/0
% 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_lte0]: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% 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_ADDu_u_RINV]: !x. h4/realax/real__add x (h4/realax/real__neg x) = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_NEGu_u_ADD]: !y x. h4/realax/real__neg (h4/realax/real__add x y) = h4/realax/real__add (h4/realax/real__neg x) (h4/realax/real__neg y)
% Assm [h4s_reals_REALu_u_MULu_u_LZERO]: !x. h4/realax/real__mul (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_LEu_u_REFL]: !x. h4/real/real__lte x x
% Assm [h4s_reals_REALu_u_LEu_u_ANTISYM]: !y x. h4/real/real__lte x y /\ h4/real/real__lte y x <=> x = y
% Assm [h4s_reals_REALu_u_LEu_u_ADD2]: !z y x w. h4/real/real__lte w x /\ h4/real/real__lte y z ==> h4/real/real__lte (h4/realax/real__add w y) (h4/realax/real__add x z)
% Assm [h4s_reals_REALu_u_LEu_u_NEG]: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm [h4s_reals_REALu_u_MULu_u_LNEG]: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_reals_realu_u_lt]: !y x. h4/realax/real__lt x y <=> ~h4/real/real__lte y x
% Assm [h4s_reals_REALu_u_LEu_u_LNEG]: !y x. h4/real/real__lte (h4/realax/real__neg x) y <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/realax/real__add x y)
% Assm [h4s_reals_REALu_u_LEu_u_NEG2]: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm [h4s_reals_REALu_u_NEGu_u_NEG]: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm [h4s_reals_REALu_u_LEu_u_RNEG]: !y x. h4/real/real__lte x (h4/realax/real__neg y) <=> h4/real/real__lte (h4/realax/real__add x y) (h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_ADDu_u_RDISTRIB]: !z y x. h4/realax/real__mul (h4/realax/real__add x y) z = h4/realax/real__add (h4/realax/real__mul x z) (h4/realax/real__mul y z)
% Assm [h4s_extreals_extrealu_u_nchotomy]: !ee. ee = h4/extreal/NegInf \/ ee = h4/extreal/PosInf \/ (?r. ee = h4/extreal/Normal r)
% Assm [h4s_extreals_extrealu_u_ofu_u_numu_u_def]: !n. h4/extreal/extreal__of__num n = h4/extreal/Normal (h4/real/real__of__num n)
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c0]: !y x. h4/extreal/extreal__add (h4/extreal/Normal x) (h4/extreal/Normal y) = h4/extreal/Normal (h4/realax/real__add x y)
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c1]: !a. h4/extreal/extreal__add h4/extreal/PosInf a = h4/extreal/PosInf
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c2]: h4/extreal/extreal__add h4/extreal/NegInf h4/extreal/PosInf = h4/extreal/PosInf
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c3]: !v2. h4/extreal/extreal__add (h4/extreal/Normal v2) h4/extreal/PosInf = h4/extreal/PosInf
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c4]: h4/extreal/extreal__add h4/extreal/NegInf h4/extreal/NegInf = h4/extreal/NegInf
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c5]: !v5. h4/extreal/extreal__add h4/extreal/NegInf (h4/extreal/Normal v5) = h4/extreal/NegInf
% Assm [h4s_extreals_extrealu_u_addu_u_defu_c6]: !v3. h4/extreal/extreal__add (h4/extreal/Normal v3) h4/extreal/NegInf = h4/extreal/NegInf
% Assm [h4s_extreals_extrealu_u_leu_u_defu_c0]: !y x. h4/extreal/extreal__le (h4/extreal/Normal x) (h4/extreal/Normal y) <=> h4/real/real__lte x y
% Assm [h4s_extreals_extrealu_u_leu_u_defu_c2]: h4/extreal/extreal__le h4/extreal/PosInf h4/extreal/PosInf <=> T
% Assm [h4s_extreals_extrealu_u_leu_u_defu_c6]: !v5. h4/extreal/extreal__le h4/extreal/PosInf (h4/extreal/Normal v5) <=> F
% Assm [h4s_extreals_extrealu_u_ltu_u_def]: !y x. h4/extreal/extreal__lt x y <=> ~h4/extreal/extreal__le y x
% Assm [h4s_extreals_extrealu_u_ainvu_u_defu_c0]: h4/extreal/extreal__ainv h4/extreal/NegInf = h4/extreal/PosInf
% Assm [h4s_extreals_extrealu_u_ainvu_u_defu_c1]: h4/extreal/extreal__ainv h4/extreal/PosInf = h4/extreal/NegInf
% Assm [h4s_extreals_extrealu_u_ainvu_u_defu_c2]: !x. h4/extreal/extreal__ainv (h4/extreal/Normal x) = h4/extreal/Normal (h4/realax/real__neg x)
% Assm [h4s_extreals_extrealu_u_ltu_u_eq]: !y x. h4/extreal/extreal__lt (h4/extreal/Normal x) (h4/extreal/Normal y) <=> h4/realax/real__lt x y
% Assm [h4s_extreals_leu_u_refl]: !x. h4/extreal/extreal__le x x
% Assm [h4s_extreals_leu_u_inftyu_c0]: !x. h4/extreal/extreal__le h4/extreal/NegInf x
% Assm [h4s_extreals_ltu_u_inftyu_c0]: !y. h4/extreal/extreal__lt h4/extreal/NegInf (h4/extreal/Normal y)
% Assm [h4s_extreals_ltu_u_inftyu_c1]: !y. h4/extreal/extreal__lt (h4/extreal/Normal y) h4/extreal/PosInf
% Assm [h4s_extreals_ltu_u_inftyu_c2]: h4/extreal/extreal__lt h4/extreal/NegInf h4/extreal/PosInf
% Assm [h4s_extreals_ltu_u_inftyu_c3]: !x. ~h4/extreal/extreal__lt x h4/extreal/NegInf
% Assm [h4s_extreals_ltu_u_inftyu_c4]: !x. ~h4/extreal/extreal__lt h4/extreal/PosInf x
% Assm [h4s_extreals_ltu_u_inftyu_c5]: !x. ~(x = h4/extreal/PosInf) <=> h4/extreal/extreal__lt x h4/extreal/PosInf
% Assm [h4s_extreals_ltu_u_inftyu_c6]: !x. ~(x = h4/extreal/NegInf) <=> h4/extreal/extreal__lt h4/extreal/NegInf x
% Assm [h4s_extreals_ltu_u_impu_u_le]: !y x. h4/extreal/extreal__lt x y ==> h4/extreal/extreal__le x y
% Assm [h4s_extreals_ltu_u_neg]: !y x. h4/extreal/extreal__lt (h4/extreal/extreal__ainv x) (h4/extreal/extreal__ainv y) <=> h4/extreal/extreal__lt y x
% Assm [h4s_extreals_leu_u_add2]: !z y x w. h4/extreal/extreal__le w x /\ h4/extreal/extreal__le y z ==> h4/extreal/extreal__le (h4/extreal/extreal__add w y) (h4/extreal/extreal__add x z)
% Assm [h4s_extreals_addu_u_rzero]: !x. h4/extreal/extreal__add x (h4/extreal/extreal__of__num h4/num/0) = x
% Assm [h4s_extreals_addu_u_lzero]: !x. h4/extreal/extreal__add (h4/extreal/extreal__of__num h4/num/0) x = x
% Assm [h4s_extreals_negu_u_0]: h4/extreal/extreal__ainv (h4/extreal/extreal__of__num h4/num/0) = h4/extreal/extreal__of__num h4/num/0
% Assm [h4s_measures_fnu_u_minusu_u_def]: !f x. h4/measure/fn__minus f x = h4/bool/COND (h4/extreal/extreal__lt (happ f x) (h4/extreal/extreal__of__num h4/num/0)) (h4/extreal/extreal__ainv (happ f x)) (h4/extreal/extreal__of__num h4/num/0)
% Goal: !_0. (!f g x0. happ (happ (happ _0 f) g) x0 = h4/extreal/extreal__add (happ f x0) (happ g x0)) ==> (!x g f. h4/extreal/extreal__le (h4/measure/fn__minus (happ (happ _0 f) g) x) (h4/extreal/extreal__add (h4/measure/fn__minus f x) (h4/measure/fn__minus g x)))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q115485,TV_Q115481]: ![V_f, V_g]: (![V_x]: s(TV_Q115481,happ(s(t_fun(TV_Q115485,TV_Q115481),V_f),s(TV_Q115485,V_x))) = s(TV_Q115481,happ(s(t_fun(TV_Q115485,TV_Q115481),V_g),s(TV_Q115485,V_x))) => s(t_fun(TV_Q115485,TV_Q115481),V_f) = s(t_fun(TV_Q115485,TV_Q115481),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f0) <=> ~ (p(s(t_bool,V_t))))).
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_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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,f0))))).
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,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
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,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
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_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_reals_REALu_u_ADDu_u_SYM, 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_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_ADDu_u_ASSOC, axiom, ![V_z, 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,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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_z)))).
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_reals_REALu_u_ADDu_u_LINV, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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_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_lte0, 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_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_ADDu_u_RINV, 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_realaxs_realu_u_neg(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_NEGu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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_MULu_u_LZERO, 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_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_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_LEu_u_ANTISYM, 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_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_reals_REALu_u_LEu_u_ADD2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_w),s(t_h4s_realaxs_real,V_x)))) & 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,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_w),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_z)))))))).
fof(ah4s_reals_REALu_u_LEu_u_NEG, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = 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_MULu_u_LNEG, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))) = 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)))))).
fof(ah4s_reals_realu_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_LEu_u_LNEG, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y))) = 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_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_LEu_u_NEG2, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = 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_NEGu_u_NEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_LEu_u_RNEG, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(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)))))).
fof(ah4s_reals_REALu_u_ADDu_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_realaxs_realu_u_add(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_realaxs_realu_u_add(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_extreals_extrealu_u_nchotomy, axiom, ![V_ee]: (s(t_h4s_extreals_extreal,V_ee) = s(t_h4s_extreals_extreal,h4s_extreals_neginf) | (s(t_h4s_extreals_extreal,V_ee) = s(t_h4s_extreals_extreal,h4s_extreals_posinf) | ?[V_r]: s(t_h4s_extreals_extreal,V_ee) = s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_r)))))).
fof(ah4s_extreals_extrealu_u_ofu_u_numu_u_def, axiom, ![V_n]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c0, axiom, ![V_y, V_x]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c1, axiom, ![V_a]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_posinf),s(t_h4s_extreals_extreal,V_a))) = s(t_h4s_extreals_extreal,h4s_extreals_posinf)).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c2, axiom, s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_posinf))) = s(t_h4s_extreals_extreal,h4s_extreals_posinf)).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c3, axiom, ![V_v2]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_v2))),s(t_h4s_extreals_extreal,h4s_extreals_posinf))) = s(t_h4s_extreals_extreal,h4s_extreals_posinf)).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c4, axiom, s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_neginf))) = s(t_h4s_extreals_extreal,h4s_extreals_neginf)).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c5, axiom, ![V_v5]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_v5))))) = s(t_h4s_extreals_extreal,h4s_extreals_neginf)).
fof(ah4s_extreals_extrealu_u_addu_u_defu_c6, axiom, ![V_v3]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_v3))),s(t_h4s_extreals_extreal,h4s_extreals_neginf))) = s(t_h4s_extreals_extreal,h4s_extreals_neginf)).
fof(ah4s_extreals_extrealu_u_leu_u_defu_c0, axiom, ![V_y, V_x]: s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_normal(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_extreals_extrealu_u_leu_u_defu_c2, axiom, s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_posinf),s(t_h4s_extreals_extreal,h4s_extreals_posinf))) = s(t_bool,t)).
fof(ah4s_extreals_extrealu_u_leu_u_defu_c6, axiom, ![V_v5]: s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_posinf),s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_v5))))) = s(t_bool,f0)).
fof(ah4s_extreals_extrealu_u_ltu_u_def, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,V_y)))) <=> ~ (p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,V_y),s(t_h4s_extreals_extreal,V_x))))))).
fof(ah4s_extreals_extrealu_u_ainvu_u_defu_c0, axiom, s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,h4s_extreals_neginf))) = s(t_h4s_extreals_extreal,h4s_extreals_posinf)).
fof(ah4s_extreals_extrealu_u_ainvu_u_defu_c1, axiom, s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,h4s_extreals_posinf))) = s(t_h4s_extreals_extreal,h4s_extreals_neginf)).
fof(ah4s_extreals_extrealu_u_ainvu_u_defu_c2, axiom, ![V_x]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_extreals_extrealu_u_ltu_u_eq, axiom, ![V_y, V_x]: s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_normal(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_extreals_leu_u_refl, axiom, ![V_x]: p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,V_x))))).
fof(ah4s_extreals_leu_u_inftyu_c0, axiom, ![V_x]: p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,V_x))))).
fof(ah4s_extreals_ltu_u_inftyu_c0, axiom, ![V_y]: p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_extreals_ltu_u_inftyu_c1, axiom, ![V_y]: p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,V_y))),s(t_h4s_extreals_extreal,h4s_extreals_posinf))))).
fof(ah4s_extreals_ltu_u_inftyu_c2, axiom, p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_posinf))))).
fof(ah4s_extreals_ltu_u_inftyu_c3, axiom, ![V_x]: ~ (p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,h4s_extreals_neginf)))))).
fof(ah4s_extreals_ltu_u_inftyu_c4, axiom, ![V_x]: ~ (p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_posinf),s(t_h4s_extreals_extreal,V_x)))))).
fof(ah4s_extreals_ltu_u_inftyu_c5, axiom, ![V_x]: (~ (s(t_h4s_extreals_extreal,V_x) = s(t_h4s_extreals_extreal,h4s_extreals_posinf)) <=> p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,h4s_extreals_posinf)))))).
fof(ah4s_extreals_ltu_u_inftyu_c6, axiom, ![V_x]: (~ (s(t_h4s_extreals_extreal,V_x) = s(t_h4s_extreals_extreal,h4s_extreals_neginf)) <=> p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,V_x)))))).
fof(ah4s_extreals_ltu_u_impu_u_le, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,V_y)))) => p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,V_y)))))).
fof(ah4s_extreals_ltu_u_neg, axiom, ![V_y, V_x]: s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,V_y))))) = s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,V_y),s(t_h4s_extreals_extreal,V_x)))).
fof(ah4s_extreals_leu_u_add2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,V_w),s(t_h4s_extreals_extreal,V_x)))) & p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,V_y),s(t_h4s_extreals_extreal,V_z))))) => p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,V_w),s(t_h4s_extreals_extreal,V_y))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,V_z)))))))).
fof(ah4s_extreals_addu_u_rzero, axiom, ![V_x]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,V_x),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_extreals_extreal,V_x)).
fof(ah4s_extreals_addu_u_lzero, axiom, ![V_x]: s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_extreals_extreal,V_x))) = s(t_h4s_extreals_extreal,V_x)).
fof(ah4s_extreals_negu_u_0, axiom, s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_measures_fnu_u_minusu_u_def, axiom, ![TV_u_27a]: ![V_f, V_x]: s(t_h4s_extreals_extreal,h4s_measures_fnu_u_minus(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f),s(TV_u_27a,V_x))) = s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f),s(TV_u_27a,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f),s(TV_u_27a,V_x))))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ch4s_measures_FNu_u_MINUSu_u_ADDu_u_LE, conjecture, ![TV_u_27a]: ![V_uu_0]: (![V_f, V_g, V_x0]: s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(TV_u_27a,t_h4s_extreals_extreal)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(TV_u_27a,t_h4s_extreals_extreal))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f))),s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_g))),s(TV_u_27a,V_x0))) = s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f),s(TV_u_27a,V_x0))),s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_g),s(TV_u_27a,V_x0))))) => ![V_x, V_g, V_f]: p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_measures_fnu_u_minus(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(TV_u_27a,t_h4s_extreals_extreal)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(t_fun(TV_u_27a,t_h4s_extreals_extreal),t_fun(TV_u_27a,t_h4s_extreals_extreal))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f))),s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_g))),s(TV_u_27a,V_x))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_add(s(t_h4s_extreals_extreal,h4s_measures_fnu_u_minus(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_f),s(TV_u_27a,V_x))),s(t_h4s_extreals_extreal,h4s_measures_fnu_u_minus(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),V_g),s(TV_u_27a,V_x)))))))))).
