%   ORIGINAL: h4/fmapal/ORL__DRESTRICT__COMPL__IMP
% 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/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !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/EQ__REFL: !x. x = x
% 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_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> 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/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/bool/LEFT__FORALL__OR__THM: !Q P. (!x. P x \/ Q) <=> (!x. P x) \/ Q
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% 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/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/bool/RIGHT__OR__OVER__AND: !C B A. B /\ C \/ A <=> (B \/ A) /\ (C \/ A)
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% 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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/option/IS__SOME__DEF_c1: h4/option/IS__SOME h4/option/NONE <=> F
% Assm: h4/option/THE__DEF: !x. h4/option/THE (h4/option/SOME x) = x
% Assm: h4/option/option__CLAUSES_c0: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/option/option__CLAUSES_c0: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/option/option__CLAUSES_c1: !x. h4/option/THE (h4/option/SOME x) = x
% Assm: h4/option/option__CLAUSES_c1: !x. h4/option/THE (h4/option/SOME x) = x
% Assm: h4/option/option__CLAUSES_c2: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/option/option__CLAUSES_c2: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/option/option__CLAUSES_c3: !x. ~(h4/option/SOME x = h4/option/NONE)
% Assm: h4/option/option__CLAUSES_c4: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm: h4/option/option__CLAUSES_c4: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm: h4/option/option__CLAUSES_c5: h4/option/IS__SOME h4/option/NONE <=> F
% Assm: h4/option/option__CLAUSES_c5: h4/option/IS__SOME h4/option/NONE <=> F
% Assm: h4/option/option__CLAUSES_c6: !x. h4/option/IS__NONE x <=> x = h4/option/NONE
% Assm: h4/option/option__CLAUSES_c7: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
% Assm: h4/option/option__CLAUSES_c7: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
% Assm: h4/option/option__CLAUSES_c8: !x. h4/option/IS__SOME x ==> h4/option/SOME (h4/option/THE x) = x
% Assm: h4/option/option__CLAUSES_c8: !x. h4/option/IS__SOME x ==> h4/option/SOME (h4/option/THE x) = x
% Assm: h4/option/option__CLAUSES_c9: !x. h4/option/option__CASE x h4/option/NONE h4/option/SOME = x
% Assm: h4/option/option__CLAUSES_c10: !x. h4/option/option__CASE x x h4/option/SOME = x
% Assm: h4/option/option__CLAUSES_c11: !x f e. h4/option/IS__NONE x ==> h4/option/option__CASE x e f = e
% Assm: h4/option/option__CLAUSES_c12: !x f e. h4/option/IS__SOME x ==> h4/option/option__CASE x e f = f (h4/option/THE x)
% Assm: h4/option/option__CLAUSES_c13: !x e. h4/option/IS__SOME x ==> h4/option/option__CASE x e h4/option/SOME = x
% Assm: h4/option/option__CLAUSES_c14: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm: h4/option/option__CLAUSES_c15: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/option/option__CLAUSES_c16: !x f. h4/option/OPTION__MAP f (h4/option/SOME x) = h4/option/SOME (f x)
% Assm: h4/option/option__CLAUSES_c17: !f. h4/option/OPTION__MAP f h4/option/NONE = h4/option/NONE
% Assm: h4/option/option__CLAUSES_c18: h4/option/OPTION__JOIN h4/option/NONE = h4/option/NONE
% Assm: h4/option/option__CLAUSES_c19: !x. h4/option/OPTION__JOIN (h4/option/SOME x) = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/pair/PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/PFORALL__THM: !P. (!x y. P x y) <=> $forall (h4/pair/UNCURRY (\x y. P x y))
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__MONO__ADD__EQ: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Assm: h4/pred__set/EXTENSION: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/pred__set/EMPTY__applied: !x. h4/pred__set/EMPTY x <=> F
% Assm: h4/pred__set/IN__INTER: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm: h4/pred__set/IN__DIFF: !x t s. h4/bool/IN x (h4/pred__set/DIFF s t) <=> h4/bool/IN x s /\ ~h4/bool/IN x t
% Assm: h4/pred__set/IN__INSERT: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm: h4/pred__set/IN__COMPL: !x s. h4/bool/IN x (h4/pred__set/COMPL s) <=> ~h4/bool/IN x s
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/LIST__TO__SET0_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/list/FOLDL0_c0: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm: h4/list/FOLDL0_c1: !x l f e. h4/list/FOLDL f e (h4/list/CONS x l) = h4/list/FOLDL f (f e x) l
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/MEM_c0: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm: h4/list/MEM_c0: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/list/REVERSE__DEF_c1: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm: h4/list/FINITE__LIST__TO__SET: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% Assm: h4/list/LIST__TO__SET__THM_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/list/LIST__TO__SET__THM_c1: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm: h4/res__quan/RES__FORALL: !f P. h4/bool/RES__FORALL P f <=> (!x. h4/bool/IN x P ==> f x)
% Assm: h4/finite__map/FDOM__FEMPTY: h4/finite__map/FDOM h4/finite__map/FEMPTY = h4/pred__set/EMPTY
% Assm: h4/finite__map/FDOM__FUPDATE: !f b a. h4/finite__map/FDOM (h4/finite__map/FUPDATE f (h4/pair/_2C a b)) = h4/pred__set/INSERT a (h4/finite__map/FDOM f)
% Assm: h4/finite__map/FAPPLY__FUPDATE__THM: !x f b a. h4/finite__map/FAPPLY (h4/finite__map/FUPDATE f (h4/pair/_2C a b)) x = h4/bool/COND (x = a) b (h4/finite__map/FAPPLY f x)
% Assm: h4/finite__map/FDOM__FINITE: !fm. h4/pred__set/FINITE (h4/finite__map/FDOM fm)
% Assm: h4/finite__map/fmap__INDUCT: !P. P h4/finite__map/FEMPTY /\ (!f. P f ==> (!x y. ~h4/bool/IN x (h4/finite__map/FDOM f) ==> P (h4/finite__map/FUPDATE f (h4/pair/_2C x y)))) ==> (!f. P f)
% Assm: h4/finite__map/fmap__EXT: !g f. f = g <=> h4/finite__map/FDOM f = h4/finite__map/FDOM g /\ (!x. h4/bool/IN x (h4/finite__map/FDOM f) ==> h4/finite__map/FAPPLY f x = h4/finite__map/FAPPLY g x)
% Assm: h4/finite__map/DRESTRICT__DEF_c0: !r f. h4/finite__map/FDOM (h4/finite__map/DRESTRICT f r) = h4/pred__set/INTER (h4/finite__map/FDOM f) r
% Assm: h4/finite__map/DRESTRICT__DEF_c1: !x r f. h4/finite__map/FAPPLY (h4/finite__map/DRESTRICT f r) x = h4/bool/COND (h4/bool/IN x (h4/pred__set/INTER (h4/finite__map/FDOM f) r)) (h4/finite__map/FAPPLY f x) (h4/finite__map/FAPPLY h4/finite__map/FEMPTY x)
% Assm: h4/finite__map/FLOOKUP__DEF: !x f. h4/finite__map/FLOOKUP f x = h4/bool/COND (h4/bool/IN x (h4/finite__map/FDOM f)) (h4/option/SOME (h4/finite__map/FAPPLY f x)) h4/option/NONE
% Assm: h4/finite__map/FLOOKUP__EMPTY: !k. h4/finite__map/FLOOKUP h4/finite__map/FEMPTY k = h4/option/NONE
% Assm: h4/finite__map/FLOOKUP__UPDATE: !v k2 k1 fm. h4/finite__map/FLOOKUP (h4/finite__map/FUPDATE fm (h4/pair/_2C k1 v)) k2 = h4/bool/COND (k1 = k2) (h4/option/SOME v) (h4/finite__map/FLOOKUP fm k2)
% Assm: h4/finite__map/FUN__FMAP__DEF: !f P. h4/pred__set/FINITE P ==> h4/finite__map/FDOM (h4/finite__map/FUN__FMAP f P) = P /\ (!x. h4/bool/IN x P ==> h4/finite__map/FAPPLY (h4/finite__map/FUN__FMAP f P) x = f x)
% Assm: h4/finite__map/FUPDATE__LIST0: h4/finite__map/FUPDATE__LIST = h4/list/FOLDL h4/finite__map/FUPDATE
% Assm: h4/finite__map/FUPDATE__LIST__APPEND: !kvl2 kvl1 fm. h4/finite__map/FUPDATE__LIST fm (h4/list/APPEND kvl1 kvl2) = h4/finite__map/FUPDATE__LIST (h4/finite__map/FUPDATE__LIST fm kvl1) kvl2
% Assm: h4/toto/cpn__case__def_c0: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/LESS v0 v1 v2 = v0
% Assm: h4/toto/cpn__case__def_c1: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm: h4/toto/cpn__case__def_c2: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm: h4/toto/cpn__case__cong: !v2_27 v2 v1_27 v1 v0_27 v0 M_27 M. M = M_27 /\ (M_27 = h4/toto/LESS ==> v0 = v0_27) /\ (M_27 = h4/toto/EQUAL ==> v1 = v1_27) /\ (M_27 = h4/toto/GREATER ==> v2 = v2_27) ==> h4/toto/cpn__CASE M v0 v1 v2 = h4/toto/cpn__CASE M_27 v0_27 v1_27 v2_27
% Assm: h4/toto/cpn__nchotomy: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm: h4/toto/all__cpn__distinct_c0: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm: h4/toto/all__cpn__distinct_c1: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm: h4/toto/all__cpn__distinct_c2: ~(h4/toto/EQUAL = h4/toto/GREATER)
% Assm: h4/toto/all__cpn__distinct_c3: ~(h4/toto/EQUAL = h4/toto/LESS)
% Assm: h4/toto/all__cpn__distinct_c4: ~(h4/toto/GREATER = h4/toto/LESS)
% Assm: h4/toto/all__cpn__distinct_c5: ~(h4/toto/GREATER = h4/toto/EQUAL)
% Assm: h4/toto/toto__equal__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Assm: h4/toto/toto__equal__imp__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL ==> x = y
% Assm: h4/toto/toto__refl: !x c. h4/toto/apto c x x = h4/toto/EQUAL
% Assm: h4/toto/toto__antisym: !y x c. h4/toto/apto c x y = h4/toto/GREATER <=> h4/toto/apto c y x = h4/toto/LESS
% Assm: h4/toto/toto__glneq_c0: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/toto__glneq_c0: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/toto__glneq_c1: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm: h4/toto/toto__glneq_c1: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm: h4/toto/totoLLtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/enumeral/OL0_c0: !cmp. h4/enumeral/OL cmp h4/list/NIL <=> T
% Assm: h4/enumeral/OL0_c1: !l cmp a. h4/enumeral/OL cmp (h4/list/CONS a l) <=> h4/enumeral/OL cmp l /\ (!p. h4/bool/IN p (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm: h4/enumeral/OL0_c1: !l cmp a. h4/enumeral/OL cmp (h4/list/CONS a l) <=> h4/enumeral/OL cmp l /\ (!p. h4/bool/IN p (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm: h4/fmapal/ORL__tupled__primitive: h4/fmapal/ORL__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b a l cmp. R (h4/pair/_2C cmp l) (h4/pair/_2C cmp (h4/list/CONS (h4/pair/_2C a b) l))))) (\ORL__tupled a_27. h4/pair/pair__CASE a_27 (\cmp v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 l. h4/pair/pair__CASE v2 (\a b. h4/combin/I (ORL__tupled (h4/pair/_2C cmp l) /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS))))))
% Assm: h4/fmapal/ORL__curried: !x1 x. h4/fmapal/ORL x x1 <=> h4/fmapal/ORL__tupled (h4/pair/_2C x x1)
% Assm: h4/fmapal/assocv__tupled__primitive: h4/fmapal/assocv__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y l x a. ~(a = x) ==> R (h4/pair/_2C l a) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C x y) l) a)))) (\assocv__tupled a_27. h4/pair/pair__CASE a_27 (\v a. h4/list/list__CASE v (h4/combin/I h4/option/NONE) (\v2 l. h4/pair/pair__CASE v2 (\x y. h4/combin/I (h4/bool/COND (a = x) (h4/option/SOME y) (assocv__tupled (h4/pair/_2C l a)))))))
% Assm: h4/fmapal/assocv__curried: !x1 x. h4/fmapal/assocv x x1 = h4/fmapal/assocv__tupled (h4/pair/_2C x x1)
% Assm: h4/fmapal/unlookup0: !f. h4/fmapal/unlookup f = h4/finite__map/FUN__FMAP (h4/combin/o h4/option/THE f) (h4/combin/o h4/option/IS__SOME f)
% Assm: h4/fmapal/fmap0: !l. h4/fmapal/fmap l = h4/finite__map/FUPDATE__LIST h4/finite__map/FEMPTY (h4/list/REVERSE l)
% Assm: h4/fmapal/fmap__FDOM: !l. h4/finite__map/FDOM (h4/fmapal/fmap l) = h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST l)
% Assm: h4/fmapal/diff__merge__tupled__primitive: h4/fmapal/diff__merge__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> R (h4/pair/_2C cmp (h4/pair/_2C l m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))))) (\diff__merge__tupled a_27. h4/pair/pair__CASE a_27 (\cmp v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (\v4 l. h4/pair/pair__CASE v4 (\a b. h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (h4/pair/_2C a b) l)) (\y m. h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/list/CONS (h4/pair/_2C a b) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))))) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m))) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))))))))
% Assm: h4/fmapal/diff__merge__curried: !x2 x1 x. h4/fmapal/diff__merge x x1 x2 = h4/fmapal/diff__merge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/fmapal/diff__merge__ind: !P. (!cmp. P cmp h4/list/NIL h4/list/NIL) /\ (!cmp a b l. P cmp (h4/list/CONS (h4/pair/_2C a b) l) h4/list/NIL) /\ (!cmp y m. P cmp h4/list/NIL (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> P cmp l m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> P cmp l (h4/list/CONS y m)) ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)) ==> (!v v1 v2. P v v1 v2)
% Goal: !l cmp. h4/fmapal/ORL cmp l ==> (!m. h4/enumeral/OL cmp m ==> h4/fmapal/ORL cmp (h4/fmapal/diff__merge cmp l m) /\ h4/fmapal/fmap (h4/fmapal/diff__merge cmp l m) = h4/finite__map/DRESTRICT (h4/fmapal/fmap l) (h4/pred__set/COMPL (h4/list/LIST__TO__SET m)))
%   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_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% 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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% 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_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !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_EQu_u_REFL]: !x. x = x
% 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_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> 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_FORALLu_u_ANDu_u_THM]: !Q P. (!x. happ P x /\ happ Q x) <=> (!x. happ P x) /\ (!x. happ Q x)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. happ P x \/ Q) <=> (!x. happ P x) \/ Q
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% 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_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_bools_RIGHTu_u_ORu_u_OVERu_u_AND]: !C B A. B /\ C \/ A <=> (B \/ A) /\ (C \/ A)
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% 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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = happ h4/option/SOME x)
% Assm [h4s_options_ISu_u_SOMEu_u_DEFu_c1]: happ h4/option/IS__SOME h4/option/NONE <=> F
% Assm [h4s_options_THEu_u_DEF]: !x. happ h4/option/THE (happ h4/option/SOME x) = x
% Assm [h4s_options_optionu_u_CLAUSESu_c0]: !y x. happ h4/option/SOME x = happ h4/option/SOME y <=> x = y
% Assm [h4s_options_optionu_u_CLAUSESu_c0]: !y x. happ h4/option/SOME x = happ h4/option/SOME y <=> x = y
% Assm [h4s_options_optionu_u_CLAUSESu_c1]: !x. happ h4/option/THE (happ h4/option/SOME x) = x
% Assm [h4s_options_optionu_u_CLAUSESu_c1]: !x. happ h4/option/THE (happ h4/option/SOME x) = x
% Assm [h4s_options_optionu_u_CLAUSESu_c2]: !x. ~(h4/option/NONE = happ h4/option/SOME x)
% Assm [h4s_options_optionu_u_CLAUSESu_c2]: !x. ~(h4/option/NONE = happ h4/option/SOME x)
% Assm [h4s_options_optionu_u_CLAUSESu_c3]: !x. ~(happ h4/option/SOME x = h4/option/NONE)
% Assm [h4s_options_optionu_u_CLAUSESu_c4]: !x. happ h4/option/IS__SOME (happ h4/option/SOME x) <=> T
% Assm [h4s_options_optionu_u_CLAUSESu_c4]: !x. happ h4/option/IS__SOME (happ h4/option/SOME x) <=> T
% Assm [h4s_options_optionu_u_CLAUSESu_c5]: happ h4/option/IS__SOME h4/option/NONE <=> F
% Assm [h4s_options_optionu_u_CLAUSESu_c5]: happ h4/option/IS__SOME h4/option/NONE <=> F
% Assm [h4s_options_optionu_u_CLAUSESu_c6]: !x. h4/option/IS__NONE x <=> x = h4/option/NONE
% Assm [h4s_options_optionu_u_CLAUSESu_c7]: !x. ~happ h4/option/IS__SOME x <=> x = h4/option/NONE
% Assm [h4s_options_optionu_u_CLAUSESu_c7]: !x. ~happ h4/option/IS__SOME x <=> x = h4/option/NONE
% Assm [h4s_options_optionu_u_CLAUSESu_c8]: !x. happ h4/option/IS__SOME x ==> happ h4/option/SOME (happ h4/option/THE x) = x
% Assm [h4s_options_optionu_u_CLAUSESu_c8]: !x. happ h4/option/IS__SOME x ==> happ h4/option/SOME (happ h4/option/THE x) = x
% Assm [h4s_options_optionu_u_CLAUSESu_c9]: !x. h4/option/option__CASE x h4/option/NONE h4/option/SOME = x
% Assm [h4s_options_optionu_u_CLAUSESu_c10]: !x. h4/option/option__CASE x x h4/option/SOME = x
% Assm [h4s_options_optionu_u_CLAUSESu_c11]: !x f e. h4/option/IS__NONE x ==> h4/option/option__CASE x e f = e
% Assm [h4s_options_optionu_u_CLAUSESu_c12]: !x f e. happ h4/option/IS__SOME x ==> h4/option/option__CASE x e f = happ f (happ h4/option/THE x)
% Assm [h4s_options_optionu_u_CLAUSESu_c13]: !x e. happ h4/option/IS__SOME x ==> h4/option/option__CASE x e h4/option/SOME = x
% Assm [h4s_options_optionu_u_CLAUSESu_c14]: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm [h4s_options_optionu_u_CLAUSESu_c15]: !x v f. h4/option/option__CASE (happ h4/option/SOME x) v f = happ f x
% Assm [h4s_options_optionu_u_CLAUSESu_c16]: !x f. h4/option/OPTION__MAP f (happ h4/option/SOME x) = happ h4/option/SOME (happ f x)
% Assm [h4s_options_optionu_u_CLAUSESu_c17]: !f. h4/option/OPTION__MAP f h4/option/NONE = h4/option/NONE
% Assm [h4s_options_optionu_u_CLAUSESu_c18]: h4/option/OPTION__JOIN h4/option/NONE = h4/option/NONE
% Assm [h4s_options_optionu_u_CLAUSESu_c19]: !x. h4/option/OPTION__JOIN (happ h4/option/SOME x) = x
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_pairs_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (happ h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_FST0]: !y x. happ h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_PFORALLu_u_THM]: !_1. (!P x y. happ (happ (happ _1 P) x) y <=> happ (happ P x) y) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!P. (!x y. happ (happ P x) y) <=> $forall (h4/pair/UNCURRY (happ _0 P))))
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ]: !p n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/_2B m p)) (h4/arithmetic/_2B n p) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Assm [h4s_predu_u_sets_EXTENSION]: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_EMPTYu_u_applied]: !x. happ h4/pred__set/EMPTY x <=> F
% Assm [h4s_predu_u_sets_INu_u_INTER]: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm [h4s_predu_u_sets_INu_u_DIFF]: !x t s. h4/bool/IN x (h4/pred__set/DIFF s t) <=> h4/bool/IN x s /\ ~h4/bool/IN x t
% Assm [h4s_predu_u_sets_INu_u_INSERT]: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm [h4s_predu_u_sets_INu_u_COMPL]: !x s. h4/bool/IN x (h4/pred__set/COMPL s) <=> ~h4/bool/IN x s
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (happ f h) (h4/list/MAP f t)
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_lists_FOLDL0u_c0]: !f e. happ (happ (h4/list/FOLDL f) e) h4/list/NIL = e
% Assm [h4s_lists_FOLDL0u_c1]: !x l f e. happ (happ (h4/list/FOLDL f) e) (h4/list/CONS x l) = happ (happ (h4/list/FOLDL f) (happ (happ f e) x)) l
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_MEMu_c0]: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm [h4s_lists_MEMu_c0]: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_REVERSEu_u_DEFu_c1]: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm [h4s_lists_FINITEu_u_LISTu_u_TOu_u_SET]: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c1]: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm [h4s_resu_u_quans_RESu_u_FORALL]: !f P. h4/bool/RES__FORALL P f <=> (!x. h4/bool/IN x P ==> happ f x)
% Assm [h4s_finiteu_u_maps_FDOMu_u_FEMPTY]: h4/finite__map/FDOM h4/finite__map/FEMPTY = h4/pred__set/EMPTY
% Assm [h4s_finiteu_u_maps_FDOMu_u_FUPDATE]: !f b a. h4/finite__map/FDOM (happ (happ h4/finite__map/FUPDATE f) (h4/pair/_2C a b)) = h4/pred__set/INSERT a (h4/finite__map/FDOM f)
% Assm [h4s_finiteu_u_maps_FAPPLYu_u_FUPDATEu_u_THM]: !x f b a. ?v. (v <=> x = a) /\ h4/finite__map/FAPPLY (happ (happ h4/finite__map/FUPDATE f) (h4/pair/_2C a b)) x = h4/bool/COND v b (h4/finite__map/FAPPLY f x)
% Assm [h4s_finiteu_u_maps_FDOMu_u_FINITE]: !fm. h4/pred__set/FINITE (h4/finite__map/FDOM fm)
% Assm [h4s_finiteu_u_maps_fmapu_u_INDUCT]: !P. happ P h4/finite__map/FEMPTY /\ (!f. happ P f ==> (!x y. ~h4/bool/IN x (h4/finite__map/FDOM f) ==> happ P (happ (happ h4/finite__map/FUPDATE f) (h4/pair/_2C x y)))) ==> (!f. happ P f)
% Assm [h4s_finiteu_u_maps_fmapu_u_EXT]: !g f. f = g <=> h4/finite__map/FDOM f = h4/finite__map/FDOM g /\ (!x. h4/bool/IN x (h4/finite__map/FDOM f) ==> h4/finite__map/FAPPLY f x = h4/finite__map/FAPPLY g x)
% Assm [h4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c0]: !r f. h4/finite__map/FDOM (h4/finite__map/DRESTRICT f r) = h4/pred__set/INTER (h4/finite__map/FDOM f) r
% Assm [h4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c1]: !x r f. h4/finite__map/FAPPLY (h4/finite__map/DRESTRICT f r) x = h4/bool/COND (h4/bool/IN x (h4/pred__set/INTER (h4/finite__map/FDOM f) r)) (h4/finite__map/FAPPLY f x) (h4/finite__map/FAPPLY h4/finite__map/FEMPTY x)
% Assm [h4s_finiteu_u_maps_FLOOKUPu_u_DEF]: !x f. h4/finite__map/FLOOKUP f x = h4/bool/COND (h4/bool/IN x (h4/finite__map/FDOM f)) (happ h4/option/SOME (h4/finite__map/FAPPLY f x)) h4/option/NONE
% Assm [h4s_finiteu_u_maps_FLOOKUPu_u_EMPTY]: !k. h4/finite__map/FLOOKUP h4/finite__map/FEMPTY k = h4/option/NONE
% Assm [h4s_finiteu_u_maps_FLOOKUPu_u_UPDATE]: !v k2 k1 fm. ?v. (v <=> k1 = k2) /\ h4/finite__map/FLOOKUP (happ (happ h4/finite__map/FUPDATE fm) (h4/pair/_2C k1 v)) k2 = h4/bool/COND v (happ h4/option/SOME v) (h4/finite__map/FLOOKUP fm k2)
% Assm [h4s_finiteu_u_maps_FUNu_u_FMAPu_u_DEF]: !f P. h4/pred__set/FINITE P ==> h4/finite__map/FDOM (h4/finite__map/FUN__FMAP f P) = P /\ (!x. h4/bool/IN x P ==> h4/finite__map/FAPPLY (h4/finite__map/FUN__FMAP f P) x = happ f x)
% Assm [h4s_finiteu_u_maps_FUPDATEu_u_LIST0]: h4/finite__map/FUPDATE__LIST = h4/list/FOLDL h4/finite__map/FUPDATE
% Assm [h4s_finiteu_u_maps_FUPDATEu_u_LISTu_u_APPEND]: !kvl2 kvl1 fm. happ (happ h4/finite__map/FUPDATE__LIST fm) (h4/list/APPEND kvl1 kvl2) = happ (happ h4/finite__map/FUPDATE__LIST (happ (happ h4/finite__map/FUPDATE__LIST fm) kvl1)) kvl2
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c0]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/LESS v0 v1 v2 = v0
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c1]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c2]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm [h4s_totos_cpnu_u_caseu_u_cong]: !v2_27 v2 v1_27 v1 v0_27 v0 M_27 M. M = M_27 /\ (M_27 = h4/toto/LESS ==> v0 = v0_27) /\ (M_27 = h4/toto/EQUAL ==> v1 = v1_27) /\ (M_27 = h4/toto/GREATER ==> v2 = v2_27) ==> h4/toto/cpn__CASE M v0 v1 v2 = h4/toto/cpn__CASE M_27 v0_27 v1_27 v2_27
% Assm [h4s_totos_cpnu_u_nchotomy]: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c0]: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c1]: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c2]: ~(h4/toto/EQUAL = h4/toto/GREATER)
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c3]: ~(h4/toto/EQUAL = h4/toto/LESS)
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c4]: ~(h4/toto/GREATER = h4/toto/LESS)
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c5]: ~(h4/toto/GREATER = h4/toto/EQUAL)
% Assm [h4s_totos_totou_u_equalu_u_eq]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Assm [h4s_totos_totou_u_equalu_u_impu_u_eq]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL ==> x = y
% Assm [h4s_totos_totou_u_refl]: !x c. h4/toto/apto c x x = h4/toto/EQUAL
% Assm [h4s_totos_totou_u_antisym]: !y x c. h4/toto/apto c x y = h4/toto/GREATER <=> h4/toto/apto c y x = h4/toto/LESS
% Assm [h4s_totos_totou_u_glnequ_c0]: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totou_u_glnequ_c0]: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totou_u_glnequ_c1]: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm [h4s_totos_totou_u_glnequ_c1]: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm [h4s_totos_totoLLtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_enumerals_OL0u_c0]: !cmp. h4/enumeral/OL cmp h4/list/NIL <=> T
% Assm [h4s_enumerals_OL0u_c1]: !l cmp a. h4/enumeral/OL cmp (h4/list/CONS a l) <=> h4/enumeral/OL cmp l /\ (!p. h4/bool/IN p (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm [h4s_enumerals_OL0u_c1]: !l cmp a. h4/enumeral/OL cmp (h4/list/CONS a l) <=> h4/enumeral/OL cmp l /\ (!p. h4/bool/IN p (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm [h4s_fmapals_ORLu_u_tupledu_u_primitive]: !_8. (!ORL__tupled l cmp a b. ?v. (v <=> happ ORL__tupled (h4/pair/_2C cmp l) /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)) /\ (happ (happ (happ (happ (happ _8 ORL__tupled) l) cmp) a) b <=> h4/combin/I v)) ==> (!_7. (!ORL__tupled l cmp a. happ (happ (happ (happ _7 ORL__tupled) l) cmp) a = happ (happ (happ (happ _8 ORL__tupled) l) cmp) a) ==> (!_6. (!v2 ORL__tupled cmp l. happ (happ (happ (happ _6 v2) ORL__tupled) cmp) l <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 ORL__tupled) l) cmp)) ==> (!_5. (!ORL__tupled cmp v2. happ (happ (happ _5 ORL__tupled) cmp) v2 = happ (happ (happ _6 v2) ORL__tupled) cmp) ==> (!_4. (!ORL__tupled cmp v1. happ (happ (happ _4 ORL__tupled) cmp) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 ORL__tupled) cmp)) ==> (!_3. (!ORL__tupled cmp. happ (happ _3 ORL__tupled) cmp = happ (happ _4 ORL__tupled) cmp) ==> (!_2. (!ORL__tupled a_27. happ (happ _2 ORL__tupled) a_27 <=> h4/pair/pair__CASE a_27 (happ _3 ORL__tupled)) ==> (!_1. (!ORL__tupled. happ _1 ORL__tupled = happ _2 ORL__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b a l cmp. happ (happ R (h4/pair/_2C cmp l)) (h4/pair/_2C cmp (h4/list/CONS (h4/pair/_2C a b) l)))) ==> h4/fmapal/ORL__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_fmapals_ORLu_u_curried]: !x1 x. h4/fmapal/ORL x x1 <=> happ h4/fmapal/ORL__tupled (h4/pair/_2C x x1)
% Assm [h4s_fmapals_assocvu_u_tupledu_u_primitive]: !_8. (!x assocv__tupled l a y. ?v. (v <=> a = x) /\ happ (happ (happ (happ (happ _8 x) assocv__tupled) l) a) y = h4/combin/I (h4/bool/COND v (happ h4/option/SOME y) (happ assocv__tupled (h4/pair/_2C l a)))) ==> (!_7. (!assocv__tupled l a x. happ (happ (happ (happ _7 assocv__tupled) l) a) x = happ (happ (happ (happ _8 x) assocv__tupled) l) a) ==> (!_6. (!v2 assocv__tupled a l. happ (happ (happ (happ _6 v2) assocv__tupled) a) l = h4/pair/pair__CASE v2 (happ (happ (happ _7 assocv__tupled) l) a)) ==> (!_5. (!assocv__tupled a v2. happ (happ (happ _5 assocv__tupled) a) v2 = happ (happ (happ _6 v2) assocv__tupled) a) ==> (!_4. (!v assocv__tupled a. happ (happ (happ _4 v) assocv__tupled) a = h4/list/list__CASE v (h4/combin/I h4/option/NONE) (happ (happ _5 assocv__tupled) a)) ==> (!_3. (!assocv__tupled v. happ (happ _3 assocv__tupled) v = happ (happ _4 v) assocv__tupled) ==> (!_2. (!assocv__tupled a_27. happ (happ _2 assocv__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 assocv__tupled)) ==> (!_1. (!assocv__tupled. happ _1 assocv__tupled = happ _2 assocv__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y l x a. ~(a = x) ==> happ (happ R (h4/pair/_2C l a)) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C x y) l) a))) ==> h4/fmapal/assocv__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_fmapals_assocvu_u_curried]: !x1 x. h4/fmapal/assocv x x1 = happ h4/fmapal/assocv__tupled (h4/pair/_2C x x1)
% Assm [h4s_fmapals_unlookup0]: !f. h4/fmapal/unlookup f = h4/finite__map/FUN__FMAP (h4/combin/o h4/option/THE f) (h4/combin/o h4/option/IS__SOME f)
% Assm [h4s_fmapals_fmap0]: !l. h4/fmapal/fmap l = happ (happ h4/finite__map/FUPDATE__LIST h4/finite__map/FEMPTY) (h4/list/REVERSE l)
% Assm [h4s_fmapals_fmapu_u_FDOM]: !l. h4/finite__map/FDOM (h4/fmapal/fmap l) = h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST l)
% Assm [h4s_fmapals_diffu_u_mergeu_u_tupledu_u_primitive]: !_12. (!y diff__merge__tupled cmp a b l m. happ (happ (happ (happ (happ (happ (happ _12 y) diff__merge__tupled) cmp) a) b) l) m = h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/list/CONS (h4/pair/_2C a b) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))))) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m))) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))) ==> (!_11. (!diff__merge__tupled cmp a b l y. happ (happ (happ (happ (happ (happ _11 diff__merge__tupled) cmp) a) b) l) y = happ (happ (happ (happ (happ (happ _12 y) diff__merge__tupled) cmp) a) b) l) ==> (!_10. (!v3 diff__merge__tupled cmp a l b. happ (happ (happ (happ (happ (happ _10 v3) diff__merge__tupled) cmp) a) l) b = h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (h4/pair/_2C a b) l)) (happ (happ (happ (happ (happ _11 diff__merge__tupled) cmp) a) b) l)) ==> (!_9. (!v3 diff__merge__tupled cmp l a. happ (happ (happ (happ (happ _9 v3) diff__merge__tupled) cmp) l) a = happ (happ (happ (happ (happ _10 v3) diff__merge__tupled) cmp) a) l) ==> (!_8. (!v4 v3 diff__merge__tupled cmp l. happ (happ (happ (happ (happ _8 v4) v3) diff__merge__tupled) cmp) l = h4/pair/pair__CASE v4 (happ (happ (happ (happ _9 v3) diff__merge__tupled) cmp) l)) ==> (!_7. (!v3 diff__merge__tupled cmp v4. happ (happ (happ (happ _7 v3) diff__merge__tupled) cmp) v4 = happ (happ (happ (happ _8 v4) v3) diff__merge__tupled) cmp) ==> (!_6. (!v2 diff__merge__tupled cmp v3. happ (happ (happ (happ _6 v2) diff__merge__tupled) cmp) v3 = h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (happ (happ (happ _7 v3) diff__merge__tupled) cmp)) ==> (!_5. (!diff__merge__tupled cmp v2. happ (happ (happ _5 diff__merge__tupled) cmp) v2 = happ (happ (happ _6 v2) diff__merge__tupled) cmp) ==> (!_4. (!diff__merge__tupled cmp v1. happ (happ (happ _4 diff__merge__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 diff__merge__tupled) cmp)) ==> (!_3. (!diff__merge__tupled cmp. happ (happ _3 diff__merge__tupled) cmp = happ (happ _4 diff__merge__tupled) cmp) ==> (!_2. (!diff__merge__tupled a_27. happ (happ _2 diff__merge__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 diff__merge__tupled)) ==> (!_1. (!diff__merge__tupled. happ _1 diff__merge__tupled = happ _2 diff__merge__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m))))) ==> h4/fmapal/diff__merge__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_fmapals_diffu_u_mergeu_u_curried]: !x2 x1 x. h4/fmapal/diff__merge x x1 x2 = happ h4/fmapal/diff__merge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_fmapals_diffu_u_mergeu_u_ind]: !P. (!cmp. happ (happ (happ P cmp) h4/list/NIL) h4/list/NIL) /\ (!cmp a b l. happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) h4/list/NIL) /\ (!cmp y m. happ (happ (happ P cmp) h4/list/NIL) (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ (happ P cmp) l) m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ (happ P cmp) l) (h4/list/CONS y m)) ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) (h4/list/CONS y m)) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
% Goal: !l cmp. h4/fmapal/ORL cmp l ==> (!m. h4/enumeral/OL cmp m ==> h4/fmapal/ORL cmp (h4/fmapal/diff__merge cmp l m) /\ h4/fmapal/fmap (h4/fmapal/diff__merge cmp l m) = h4/finite__map/DRESTRICT (h4/fmapal/fmap l) (h4/pred__set/COMPL (h4/list/LIST__TO__SET m)))
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_Q220477,TV_Q220473]: ![V_f, V_g]: (![V_x]: s(TV_Q220473,happ(s(t_fun(TV_Q220477,TV_Q220473),V_f),s(TV_Q220477,V_x))) = s(TV_Q220473,happ(s(t_fun(TV_Q220477,TV_Q220473),V_g),s(TV_Q220477,V_x))) => s(t_fun(TV_Q220477,TV_Q220473),V_f) = s(t_fun(TV_Q220477,TV_Q220473),V_g))).
fof(ah4s_bools_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_x)))))).
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_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_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,f)) => 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_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_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_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_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,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,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_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_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_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_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_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,f) <=> ~ (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,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_FORALLu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (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_Q),s(TV_u_27a,V_x))))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((![V_x]: 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,V_Q))) <=> ![V_x]: (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,V_Q))))).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (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,V_Q))) <=> (![V_x]: 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,V_Q))))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) | ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
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_bools_LEFTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) & p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) & (p(s(t_bool,V_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: (((p(s(t_bool,V_B)) & p(s(t_bool,V_C))) | p(s(t_bool,V_A))) <=> ((p(s(t_bool,V_B)) | p(s(t_bool,V_A))) & (p(s(t_bool,V_C)) | p(s(t_bool,V_A)))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_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_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,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_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_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_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_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))).
fof(ah4s_options_ISu_u_SOMEu_u_DEFu_c1, axiom, ![TV_u_27a]: s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,f)).
fof(ah4s_options_THEu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ah4s_options_optionu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_options_optionu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_options_optionu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ah4s_options_optionu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ah4s_options_optionu_u_CLAUSESu_c2, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))).
fof(ah4s_options_optionu_u_CLAUSESu_c2, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))).
fof(ah4s_options_optionu_u_CLAUSESu_c3, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
fof(ah4s_options_optionu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(t_bool,t)).
fof(ah4s_options_optionu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(t_bool,t)).
fof(ah4s_options_optionu_u_CLAUSESu_c5, axiom, ![TV_u_27a]: s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,f)).
fof(ah4s_options_optionu_u_CLAUSESu_c5, axiom, ![TV_u_27a]: s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,f)).
fof(ah4s_options_optionu_u_CLAUSESu_c6, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(TV_u_27a),V_x)))) <=> s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
fof(ah4s_options_optionu_u_CLAUSESu_c7, axiom, ![TV_u_27a]: ![V_x]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x))))) <=> s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
fof(ah4s_options_optionu_u_CLAUSESu_c7, axiom, ![TV_u_27a]: ![V_x]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x))))) <=> s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
fof(ah4s_options_optionu_u_CLAUSESu_c8, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x)))) => s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),V_x))))) = s(t_h4s_options_option(TV_u_27a),V_x))).
fof(ah4s_options_optionu_u_CLAUSESu_c8, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x)))) => s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),V_x))))) = s(t_h4s_options_option(TV_u_27a),V_x))).
fof(ah4s_options_optionu_u_CLAUSESu_c9, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),V_x),s(t_h4s_options_option(TV_u_27a),h4s_options_none),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some))) = s(t_h4s_options_option(TV_u_27a),V_x)).
fof(ah4s_options_optionu_u_CLAUSESu_c10, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),V_x),s(t_h4s_options_option(TV_u_27a),V_x),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some))) = s(t_h4s_options_option(TV_u_27a),V_x)).
fof(ah4s_options_optionu_u_CLAUSESu_c11, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_f, V_e]: (p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(TV_u_27a),V_x)))) => s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),V_x),s(TV_u_27b,V_e),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,V_e))).
fof(ah4s_options_optionu_u_CLAUSESu_c12, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f, V_e]: (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x)))) => s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),V_x),s(TV_u_27b,V_e),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27a),h4s_options_the),s(t_h4s_options_option(TV_u_27a),V_x))))))).
fof(ah4s_options_optionu_u_CLAUSESu_c13, axiom, ![TV_u_27a]: ![V_x, V_e]: (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),h4s_options_isu_u_some),s(t_h4s_options_option(TV_u_27a),V_x)))) => s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),V_x),s(t_h4s_options_option(TV_u_27a),V_e),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some))) = s(t_h4s_options_option(TV_u_27a),V_x))).
fof(ah4s_options_optionu_u_CLAUSESu_c14, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_none),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_options_optionu_u_CLAUSESu_c15, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_options_optionu_u_CLAUSESu_c16, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))) = s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),h4s_options_some),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_options_optionu_u_CLAUSESu_c17, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_h4s_options_option(TV_u_27b),h4s_options_none)).
fof(ah4s_options_optionu_u_CLAUSESu_c18, axiom, ![TV_u_27a]: s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_join(s(t_h4s_options_option(t_h4s_options_option(TV_u_27a)),h4s_options_none))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none)).
fof(ah4s_options_optionu_u_CLAUSESu_c19, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_join(s(t_h4s_options_option(t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_h4s_options_option(t_h4s_options_option(TV_u_27a))),h4s_options_some),s(t_h4s_options_option(TV_u_27a),V_x))))) = s(t_h4s_options_option(TV_u_27a),V_x)).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_pairs_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_PFORALLu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x, V_y]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))) => ![V_P]: (![V_x, V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> p(s(t_bool,d_forall(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P)))))))))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_addu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ah4s_predu_u_sets_EXTENSION, axiom, ![TV_u_27a]: ![V_t, V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t) <=> ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_predu_u_sets_EMPTYu_u_applied, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(TV_u_27a,V_x))) = s(t_bool,f)).
fof(ah4s_predu_u_sets_INu_u_INTER, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_INu_u_DIFF, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_diff(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t)))))))).
fof(ah4s_predu_u_sets_INu_u_INSERT, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_INu_u_COMPL, axiom, ![TV_u_27a]: ![V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_compl(s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_lists_FOLDL0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f))),s(TV_u_27b,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_lists_FOLDL0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f))),s(TV_u_27b,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e))),s(TV_u_27a,V_x))))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_MEMu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(t_bool,f)).
fof(ah4s_lists_MEMu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(t_bool,f)).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_lists_FINITEu_u_LISTu_u_TOu_u_SET, axiom, ![TV_u_27a]: ![V_l]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_h),s(t_h4s_lists_list(TV_u_27b),V_t))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_h),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),V_t)))))).
fof(ah4s_resu_u_quans_RESu_u_FORALL, axiom, ![TV_u_27a]: ![V_f, V_P]: (p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))))))).
fof(ah4s_finiteu_u_maps_FDOMu_u_FEMPTY, axiom, ![TV_u_27b,TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_finiteu_u_maps_FDOMu_u_FUPDATE, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_b, V_a]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdate),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_a),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f)))))).
fof(ah4s_finiteu_u_maps_FAPPLYu_u_FUPDATEu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f, V_b, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_a)) & s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdate),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))))),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27b,V_b),s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))))).
fof(ah4s_finiteu_u_maps_FDOMu_u_FINITE, axiom, ![TV_u_27a,TV_u_27b]: ![V_fm]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm))))))).
fof(ah4s_finiteu_u_maps_fmapu_u_INDUCT, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty)))) & ![V_f]: (p(s(t_bool,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f)))) => ![V_x, V_y]: (~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdate),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))))))))) => ![V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f)))))).
fof(ah4s_finiteu_u_maps_fmapu_u_EXT, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g) <=> (s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g))) & ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f)))))) => s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x))))))).
fof(ah4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_r))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_bool),V_r)))).
fof(ah4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_r, V_f]: s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_r))),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_bool),V_r))))),s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty),s(TV_u_27a,V_x)))))).
fof(ah4s_finiteu_u_maps_FLOOKUPu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_f]: s(t_h4s_options_option(TV_u_27b),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27b),h4s_bools_cond(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))))),s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),h4s_options_some),s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(t_h4s_options_option(TV_u_27b),h4s_options_none)))).
fof(ah4s_finiteu_u_maps_FLOOKUPu_u_EMPTY, axiom, ![TV_u_27b,TV_u_27a]: ![V_k]: s(t_h4s_options_option(TV_u_27a),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fempty),s(TV_u_27b,V_k))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none)).
fof(ah4s_finiteu_u_maps_FLOOKUPu_u_UPDATE, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_k2, V_k1, V_fm]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(TV_u_27b,V_k1) = s(TV_u_27b,V_k2)) & s(t_h4s_options_option(TV_u_27a),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a))),h4s_finiteu_u_maps_fupdate),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_fm))),s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27b,V_k1),s(TV_u_27a,V_v))))),s(TV_u_27b,V_k2))) = s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_v0),s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_v))),s(t_h4s_options_option(TV_u_27a),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_fm),s(TV_u_27b,V_k2))))))).
fof(ah4s_finiteu_u_maps_FUNu_u_FMAPu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_P]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_P)))) => (s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funu_u_fmap(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_P))))) = s(t_fun(TV_u_27a,t_bool),V_P) & ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) => s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funu_u_fmap(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))))).
fof(ah4s_finiteu_u_maps_FUPDATEu_u_LIST0, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list) = s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_lists_foldl(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdate)))).
fof(ah4s_finiteu_u_maps_FUPDATEu_u_LISTu_u_APPEND, axiom, ![TV_u_27a,TV_u_27b]: ![V_kvl2, V_kvl1, V_fm]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_kvl1),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_kvl2))))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_kvl1))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_kvl2)))).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_less),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v0)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_equal),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v1)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_greater),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v2)).
fof(ah4s_totos_cpnu_u_caseu_u_cong, axiom, ![TV_u_27a]: ![V_v2u_27, V_v2, V_v1u_27, V_v1, V_v0u_27, V_v0, V_Mu_27, V_M]: ((s(t_h4s_totos_cpn,V_M) = s(t_h4s_totos_cpn,V_Mu_27) & ((s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_less) => s(TV_u_27a,V_v0) = s(TV_u_27a,V_v0u_27)) & ((s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_equal) => s(TV_u_27a,V_v1) = s(TV_u_27a,V_v1u_27)) & (s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_greater) => s(TV_u_27a,V_v2) = s(TV_u_27a,V_v2u_27))))) => s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,V_M),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,V_Mu_27),s(TV_u_27a,V_v0u_27),s(TV_u_27a,V_v1u_27),s(TV_u_27a,V_v2u_27))))).
fof(ah4s_totos_cpnu_u_nchotomy, axiom, ![V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_less) | (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_equal) | s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_greater)))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c0, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c1, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c2, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c3, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c4, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_greater) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c5, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_greater) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_totos_totou_u_equalu_u_eq, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_totos_totou_u_equalu_u_impu_u_eq, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_totos_totou_u_refl, axiom, ![TV_u_27a]: ![V_x, V_c]: s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_equal)).
fof(ah4s_totos_totou_u_antisym, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_totou_u_glnequ_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_glnequ_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_glnequ_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_glnequ_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totoLLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_enumerals_OL0u_c0, axiom, ![TV_u_27a]: ![V_cmp]: s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_enumerals_OL0u_c1, axiom, ![TV_u_27a]: ![V_l, V_cmp, V_a]: (p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a),s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> (p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l)))) & ![V_p]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_p),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_p))) = s(t_h4s_totos_cpn,h4s_totos_less))))).
fof(ah4s_enumerals_OL0u_c1, axiom, ![TV_u_27a]: ![V_l, V_cmp, V_a]: (p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a),s(t_h4s_lists_list(TV_u_27a),V_l)))))) <=> (p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l)))) & ![V_p]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_p),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_p))) = s(t_h4s_totos_cpn,h4s_totos_less))))).
fof(ah4s_fmapals_ORLu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_8]: (![V_ORLu_u_tupled, V_l, V_cmp, V_a, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) & ![V_p, V_q]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_p),s(TV_u_27b,V_q))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_p))) = s(t_h4s_totos_cpn,h4s_totos_less)))) & s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_ORLu_u_tupled, V_l, V_cmp, V_a]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_v2, V_ORLu_u_tupled, V_cmp, V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_ORLu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_ORLu_u_tupled, V_cmp, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_ORLu_u_tupled, V_cmp]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_ORLu_u_tupled, V_au_27]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_au_27))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_au_27),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))))) => ![V_uu_1]: (![V_ORLu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) & ![V_b, V_a, V_l, V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1))))))))))))).
fof(ah4s_fmapals_ORLu_u_curried, axiom, ![TV_u_27a,TV_u_27b]: ![V_x1, V_x]: s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1)))))).
fof(ah4s_fmapals_assocvu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_8]: (![V_x, V_assocvu_u_tupled, V_l, V_a, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) & s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_8),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))),s(TV_u_27b,V_y))) = s(t_h4s_options_option(TV_u_27b),h4s_combins_i(s(t_h4s_options_option(TV_u_27b),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),h4s_options_some),s(TV_u_27b,V_y))),s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_a)))))))))) => ![V_uu_7]: (![V_assocvu_u_tupled, V_l, V_a, V_x]: s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_8),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_v2, V_assocvu_u_tupled, V_a, V_l]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_options_option(TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))))) => ![V_uu_5]: (![V_assocvu_u_tupled, V_a, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))) => ![V_uu_4]: (![V_v, V_assocvu_u_tupled, V_a]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))) = s(t_h4s_options_option(TV_u_27b),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v),s(t_h4s_options_option(TV_u_27b),h4s_combins_i(s(t_h4s_options_option(TV_u_27b),h4s_options_none))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))))) => ![V_uu_3]: (![V_assocvu_u_tupled, V_v]: s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))) = s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) => ![V_uu_2]: (![V_assocvu_u_tupled, V_au_27]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_au_27))) = s(t_h4s_options_option(TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_au_27),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))))) => ![V_uu_1]: (![V_assocvu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R)))) & ![V_y, V_l, V_x, V_a]: (~ (s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_a))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_fmapals_assocvu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_1))))))))))))).
fof(ah4s_fmapals_assocvu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x1, V_x]: s(t_h4s_options_option(TV_u_27b),h4s_fmapals_assocv(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x),s(TV_u_27a,V_x1))) = s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_fmapals_assocvu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x),s(TV_u_27a,V_x1)))))).
fof(ah4s_fmapals_unlookup0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_unlookup(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),V_f))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funu_u_fmap(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(t_h4s_options_option(TV_u_27b),TV_u_27b),h4s_options_the),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_h4s_options_option(TV_u_27b),t_bool),h4s_options_isu_u_some),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),V_f)))))).
fof(ah4s_fmapals_fmap0, axiom, ![TV_u_27a,TV_u_27b]: ![V_l]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))).
fof(ah4s_fmapals_fmapu_u_FDOM, axiom, ![TV_u_27a,TV_u_27b]: ![V_l]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))).
fof(ah4s_fmapals_diffu_u_mergeu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_12]: (![V_y, V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_b, V_l, V_m]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) => ![V_uu_11]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_b, V_l, V_y]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_y))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) => ![V_uu_10]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_l, V_b]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27b,V_b))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v3),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) => ![V_uu_9]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_l, V_a]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) => ![V_uu_8]: (![V_v4, V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_l]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) => ![V_uu_7]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_6]: (![V_v2, V_diffu_u_mergeu_u_tupled, V_cmp, V_v3]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_v3))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_diffu_u_mergeu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_diffu_u_mergeu_u_tupled, V_au_27]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))))) => ![V_uu_1]: (![V_diffu_u_mergeu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) & (![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & (![V_m, V_l, V_b, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & ![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_diffu_u_mergeu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1))))))))))))))))).
fof(ah4s_fmapals_diffu_u_mergeu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_diffu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x2))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x2)))))))).
fof(ah4s_fmapals_diffu_u_mergeu_u_ind, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_a, V_b, V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_y, V_m]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))) & ![V_cmp, V_a, V_b, V_l, V_y, V_m]: (((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_v))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))),s(t_h4s_lists_list(TV_u_27a),V_v2)))))).
fof(ch4s_fmapals_ORLu_u_DRESTRICTu_u_COMPLu_u_IMP, conjecture, ![TV_u_27b,TV_u_27a]: ![V_l, V_cmp]: (p(s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))) => ![V_m]: (p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_m)))) => (p(s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_diffu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m)))))) & s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_diffu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_compl(s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_m))))))))))).
