%   ORIGINAL: h4/fmapal/optry__list0_c1
% 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/fmapal/optry__list__curried: !x1 x. h4/fmapal/optry__list x x1 = h4/fmapal/optry__list__tupled (h4/pair/_2C x x1)
% Assm: h4/fmapal/optry__list__tupled__primitive: h4/fmapal/optry__list__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l f. R (h4/pair/_2C f l) (h4/pair/_2C f (h4/list/CONS h4/option/NONE l))) /\ (!z l f. R (h4/pair/_2C f l) (h4/pair/_2C f (h4/list/CONS (h4/option/SOME z) l))))) (\optry__list__tupled a. h4/pair/pair__CASE a (\f v1. h4/list/list__CASE v1 (h4/combin/I h4/option/NONE) (\v2 l. h4/option/option__CASE v2 (h4/combin/I (optry__list__tupled (h4/pair/_2C f l))) (\z. h4/combin/I (h4/fmapal/optry (f z) (optry__list__tupled (h4/pair/_2C f l)))))))
% Assm: h4/fmapal/optry__list__ind: !P. (!f. P f h4/list/NIL) /\ (!f l. P f l ==> P f (h4/list/CONS h4/option/NONE l)) /\ (!f z l. P f l ==> P f (h4/list/CONS (h4/option/SOME z) l)) ==> (!v v1. P v v1)
% Assm: h4/option/option__Axiom: !f e. ?fn. fn h4/option/NONE = e /\ (!x. fn (h4/option/SOME x) = f x)
% Assm: h4/fmapal/optry__list0_c0: !f. h4/fmapal/optry__list f h4/list/NIL = h4/option/NONE
% Assm: h4/option/OPTION__BIND__def_c1: !x f. h4/option/OPTION__BIND (h4/option/SOME x) f = f x
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 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__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/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/basicSize/option__size__def_c1: !x f. h4/basicSize/option__size f (h4/option/SOME x) = h4/num/SUC (f x)
% 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__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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/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/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% 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/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/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% 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/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/basicSize/option__size__def_c0: !f. h4/basicSize/option__size f h4/option/NONE = h4/num/0
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% 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/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h 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_c1: ~T <=> F
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/option/option__case__def_c1: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/option/option__case__def_c0: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% 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/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% 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/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/enumeral/incr__smerge__tupled__primitive: h4/enumeral/incr__smerge__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!lol m l cmp. R (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol)) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS (h4/option/SOME m) lol)))))) (\incr__smerge__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\l v3. h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (h4/option/SOME l) h4/list/NIL)) (\v4 lol. h4/option/option__CASE v4 (h4/combin/I (h4/list/CONS (h4/option/SOME l) lol)) (\m. h4/combin/I (h4/list/CONS h4/option/NONE (incr__smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol)))))))))
% Assm: h4/enumeral/smerge__out__tupled__primitive: h4/enumeral/smerge__out__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!lol l cmp. R (h4/pair/_2C cmp (h4/pair/_2C l lol)) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS h4/option/NONE lol)))) /\ (!lol m l cmp. R (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol)) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS (h4/option/SOME m) lol)))))) (\smerge__out__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\l v3. h4/list/list__CASE v3 (h4/combin/I l) (\v4 lol. h4/option/option__CASE v4 (h4/combin/I (smerge__out__tupled (h4/pair/_2C cmp (h4/pair/_2C l lol)))) (\m. h4/combin/I (smerge__out__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol))))))))
% Assm: h4/enumeral/incr__smerge0_c2: !m lol l cmp. h4/enumeral/incr__smerge cmp l (h4/list/CONS (h4/option/SOME m) lol) = h4/list/CONS h4/option/NONE (h4/enumeral/incr__smerge cmp (h4/enumeral/smerge cmp l m) lol)
% Assm: h4/enumeral/lol__set__primitive: h4/enumeral/lol__set = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!lol. R lol (h4/list/CONS h4/option/NONE lol)) /\ (!m lol. R lol (h4/list/CONS (h4/option/SOME m) lol)))) (\lol__set a. h4/list/list__CASE a (h4/combin/I h4/pred__set/EMPTY) (\v lol. h4/option/option__CASE v (h4/combin/I (lol__set lol)) (\m. h4/combin/I (h4/pred__set/UNION (h4/list/LIST__TO__SET m) (lol__set lol)))))
% Assm: h4/enumeral/OL__sublists__tupled__primitive: h4/enumeral/OL__sublists__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!lol cmp. R (h4/pair/_2C cmp lol) (h4/pair/_2C cmp (h4/list/CONS h4/option/NONE lol))) /\ (!m lol cmp. R (h4/pair/_2C cmp lol) (h4/pair/_2C cmp (h4/list/CONS (h4/option/SOME m) lol))))) (\OL__sublists__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 lol. h4/option/option__CASE v2 (h4/combin/I (OL__sublists__tupled (h4/pair/_2C cmp lol))) (\m. h4/combin/I (h4/enumeral/OL cmp m /\ OL__sublists__tupled (h4/pair/_2C cmp lol))))))
% Assm: h4/enumeral/smerge__out0_c1: !lol l cmp. h4/enumeral/smerge__out cmp l (h4/list/CONS h4/option/NONE lol) = h4/enumeral/smerge__out cmp l lol
% Assm: h4/enumeral/incr__smerge0_c1: !lol l cmp. h4/enumeral/incr__smerge cmp l (h4/list/CONS h4/option/NONE lol) = h4/list/CONS (h4/option/SOME l) lol
% Assm: h4/enumeral/lol__set0_c1: !lol. h4/enumeral/lol__set (h4/list/CONS h4/option/NONE lol) = h4/enumeral/lol__set lol
% Assm: h4/enumeral/OL__sublists0_c1: !lol cmp. h4/enumeral/OL__sublists cmp (h4/list/CONS h4/option/NONE lol) <=> h4/enumeral/OL__sublists cmp lol
% Assm: h4/string/DEST__STRING__def_c0: h4/string/DEST__STRING h4/list/NIL = h4/option/NONE
% Assm: h4/enumeral/OL__sublists__ind: !P. (!cmp. P cmp h4/list/NIL) /\ (!cmp lol. P cmp lol ==> P cmp (h4/list/CONS h4/option/NONE lol)) /\ (!cmp m lol. P cmp lol ==> P cmp (h4/list/CONS (h4/option/SOME m) lol)) ==> (!v v1. P v v1)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/enumeral/smerge__out__ind: !P. (!cmp l. P cmp l h4/list/NIL) /\ (!cmp l lol. P cmp l lol ==> P cmp l (h4/list/CONS h4/option/NONE lol)) /\ (!cmp l m lol. P cmp (h4/enumeral/smerge cmp l m) lol ==> P cmp l (h4/list/CONS (h4/option/SOME m) lol)) ==> (!v v1 v2. P v v1 v2)
% Assm: h4/enumeral/lol__set__ind: !P. P h4/list/NIL /\ (!lol. P lol ==> P (h4/list/CONS h4/option/NONE lol)) /\ (!m lol. P lol ==> P (h4/list/CONS (h4/option/SOME m) lol)) ==> (!v. P v)
% Assm: h4/enumeral/incr__smerge__ind: !P. (!cmp l. P cmp l h4/list/NIL) /\ (!cmp l lol. P cmp l (h4/list/CONS h4/option/NONE lol)) /\ (!cmp l m lol. P cmp (h4/enumeral/smerge cmp l m) lol ==> P cmp l (h4/list/CONS (h4/option/SOME m) lol)) ==> (!v v1 v2. P v v1 v2)
% Assm: h4/string/EXTRACT__def_c0: !s i. h4/string/EXTRACT (h4/pair/_2C s (h4/pair/_2C i h4/option/NONE)) = h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i (h4/arithmetic/_2D (h4/list/LENGTH s) i)))
% Assm: h4/string/DEST__STRING__LEMS_c0: !s. h4/string/DEST__STRING s = h4/option/NONE <=> s = h4/list/NIL
% Assm: h4/string/EXTRACT__ind: !P. (!s i. P (h4/pair/_2C s (h4/pair/_2C i h4/option/NONE))) /\ (!s i n. P (h4/pair/_2C s (h4/pair/_2C i (h4/option/SOME n)))) ==> (!v v1 v2. P (h4/pair/_2C v (h4/pair/_2C v1 v2)))
% Assm: h4/option/option__case__ID: !x. h4/option/option__CASE x h4/option/NONE h4/option/SOME = x
% Assm: h4/option/NONE__DEF: h4/option/NONE = h4/option/option__ABS (h4/sum/INR h4/one/one0)
% Assm: h4/option/OPTION__GUARD__COND: !b. h4/option/OPTION__GUARD b = h4/bool/COND b (h4/option/SOME h4/one/one0) h4/option/NONE
% Assm: h4/finite__map/SUBMAP__FUPDATE__FLOOKUP: !y x f. h4/finite__map/SUBMAP f (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) <=> h4/finite__map/FLOOKUP f x = h4/option/NONE \/ h4/finite__map/FLOOKUP f x = h4/option/SOME y
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/option/SOME__11: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/enumeral/incr__smerge__curried: !x2 x1 x. h4/enumeral/incr__smerge x x1 x2 = h4/enumeral/incr__smerge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/string/EXTRACT__primitive__def: h4/string/EXTRACT = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\EXTRACT a. h4/pair/pair__CASE a (\s v1. h4/pair/pair__CASE v1 (\i v3. h4/option/option__CASE v3 (h4/combin/I (h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i (h4/arithmetic/_2D (h4/list/LENGTH s) i))))) (\n. h4/combin/I (h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i n)))))))
% Assm: h4/enumeral/smerge__out__curried: !x2 x1 x. h4/enumeral/smerge__out x x1 x2 = h4/enumeral/smerge__out__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/enumeral/OL__sublists__curried: !x1 x. h4/enumeral/OL__sublists x x1 <=> h4/enumeral/OL__sublists__tupled (h4/pair/_2C x x1)
% Assm: h4/finite__map/SUBMAP__FUPDATE__EQN: !y x f. h4/finite__map/SUBMAP f (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) <=> ~h4/bool/IN x (h4/finite__map/FDOM f) \/ h4/finite__map/FAPPLY f x = y /\ h4/bool/IN x (h4/finite__map/FDOM f)
% 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/bool/CONJ__COMM: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/option/IF__EQUALS__OPTION_c0: !x P. h4/bool/COND P (h4/option/SOME x) h4/option/NONE = h4/option/NONE <=> ~P
% Assm: h4/option/IF__EQUALS__OPTION_c2: !y x P. h4/bool/COND P (h4/option/SOME x) h4/option/NONE = h4/option/SOME y <=> P /\ x = y
% Assm: h4/marker/AC__DEF: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% 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/option/OPTION__GUARD__def_c1: h4/option/OPTION__GUARD F = h4/option/NONE
% Assm: h4/option/OPTION__GUARD__def_c0: h4/option/OPTION__GUARD T = h4/option/SOME h4/one/one0
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/string/DEST__STRING__def_c1: !rst c. h4/string/DEST__STRING (h4/list/CONS c rst) = h4/option/SOME (h4/pair/_2C c rst)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/list/NOT__NIL__CONS: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/option/NOT__NONE__SOME: !x. ~(h4/option/NONE = h4/option/SOME x)
% Goal: !l f. h4/fmapal/optry__list f (h4/list/CONS h4/option/NONE l) = h4/fmapal/optry__list f l
%   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_fmapals_optryu_u_listu_u_curried]: !x1 x. h4/fmapal/optry__list x x1 = happ h4/fmapal/optry__list__tupled (h4/pair/_2C x x1)
% Assm [h4s_fmapals_optryu_u_listu_u_tupledu_u_primitive]: !_7. (!optry__list__tupled f l z. happ (happ (happ (happ _7 optry__list__tupled) f) l) z = h4/combin/I (h4/fmapal/optry (happ f z) (happ optry__list__tupled (h4/pair/_2C f l)))) ==> (!_6. (!v2 optry__list__tupled f l. happ (happ (happ (happ _6 v2) optry__list__tupled) f) l = h4/option/option__CASE v2 (h4/combin/I (happ optry__list__tupled (h4/pair/_2C f l))) (happ (happ (happ _7 optry__list__tupled) f) l)) ==> (!_5. (!optry__list__tupled f v2. happ (happ (happ _5 optry__list__tupled) f) v2 = happ (happ (happ _6 v2) optry__list__tupled) f) ==> (!_4. (!optry__list__tupled f v1. happ (happ (happ _4 optry__list__tupled) f) v1 = h4/list/list__CASE v1 (h4/combin/I h4/option/NONE) (happ (happ _5 optry__list__tupled) f)) ==> (!_3. (!optry__list__tupled f. happ (happ _3 optry__list__tupled) f = happ (happ _4 optry__list__tupled) f) ==> (!_2. (!optry__list__tupled a. happ (happ _2 optry__list__tupled) a = h4/pair/pair__CASE a (happ _3 optry__list__tupled)) ==> (!_1. (!optry__list__tupled. happ _1 optry__list__tupled = happ _2 optry__list__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l f. happ (happ R (h4/pair/_2C f l)) (h4/pair/_2C f (h4/list/CONS h4/option/NONE l))) /\ (!z l f. happ (happ R (h4/pair/_2C f l)) (h4/pair/_2C f (h4/list/CONS (happ h4/option/SOME z) l)))) ==> h4/fmapal/optry__list__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))
% Assm [h4s_fmapals_optryu_u_listu_u_ind]: !P. (!f. happ (happ P f) h4/list/NIL) /\ (!f l. happ (happ P f) l ==> happ (happ P f) (h4/list/CONS h4/option/NONE l)) /\ (!f z l. happ (happ P f) l ==> happ (happ P f) (h4/list/CONS (happ h4/option/SOME z) l)) ==> (!v v1. happ (happ P v) v1)
% Assm [h4s_options_optionu_u_Axiom]: !f e. ?fn. happ fn h4/option/NONE = e /\ (!x. happ fn (happ h4/option/SOME x) = happ f x)
% Assm [h4s_fmapals_optryu_u_list0u_c0]: !f. h4/fmapal/optry__list f h4/list/NIL = h4/option/NONE
% Assm [h4s_options_OPTIONu_u_BINDu_u_defu_c1]: !x f. h4/option/OPTION__BIND (happ h4/option/SOME x) f = happ f x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 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_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_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_basicSizes_optionu_u_sizeu_u_defu_c1]: !x f. h4/basicSize/option__size f (happ h4/option/SOME x) = h4/num/SUC (happ f x)
% 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_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% 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_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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_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_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% 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_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_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% 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_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_basicSizes_optionu_u_sizeu_u_defu_c0]: !f. h4/basicSize/option__size f h4/option/NONE = h4/num/0
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_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_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_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% 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_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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_addu_c1]: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = happ h4/option/SOME x)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h 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_c1]: ~T <=> F
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_options_optionu_u_caseu_u_defu_c1]: !x v f. h4/option/option__CASE (happ h4/option/SOME x) v f = happ f x
% Assm [h4s_options_optionu_u_caseu_u_defu_c0]: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% 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_combins_Iu_u_THM]: !x. h4/combin/I x = x
% 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_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (h4/list/CONS a0 a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% 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_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_enumerals_incru_u_smergeu_u_tupledu_u_primitive]: !_9. (!incr__smerge__tupled cmp l lol m. happ (happ (happ (happ (happ _9 incr__smerge__tupled) cmp) l) lol) m = h4/combin/I (h4/list/CONS h4/option/NONE (happ incr__smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol))))) ==> (!_8. (!v4 incr__smerge__tupled cmp l lol. happ (happ (happ (happ (happ _8 v4) incr__smerge__tupled) cmp) l) lol = h4/option/option__CASE v4 (h4/combin/I (h4/list/CONS (happ h4/option/SOME l) lol)) (happ (happ (happ (happ _9 incr__smerge__tupled) cmp) l) lol)) ==> (!_7. (!incr__smerge__tupled cmp l v4. happ (happ (happ (happ _7 incr__smerge__tupled) cmp) l) v4 = happ (happ (happ (happ _8 v4) incr__smerge__tupled) cmp) l) ==> (!_6. (!incr__smerge__tupled cmp l v3. happ (happ (happ (happ _6 incr__smerge__tupled) cmp) l) v3 = h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (happ h4/option/SOME l) h4/list/NIL)) (happ (happ (happ _7 incr__smerge__tupled) cmp) l)) ==> (!_5. (!incr__smerge__tupled cmp l. happ (happ (happ _5 incr__smerge__tupled) cmp) l = happ (happ (happ _6 incr__smerge__tupled) cmp) l) ==> (!_4. (!incr__smerge__tupled cmp v1. happ (happ (happ _4 incr__smerge__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 incr__smerge__tupled) cmp)) ==> (!_3. (!incr__smerge__tupled cmp. happ (happ _3 incr__smerge__tupled) cmp = happ (happ _4 incr__smerge__tupled) cmp) ==> (!_2. (!incr__smerge__tupled a. happ (happ _2 incr__smerge__tupled) a = h4/pair/pair__CASE a (happ _3 incr__smerge__tupled)) ==> (!_1. (!incr__smerge__tupled. happ _1 incr__smerge__tupled = happ _2 incr__smerge__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!lol m l cmp. happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol))) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS (happ h4/option/SOME m) lol))))) ==> h4/enumeral/incr__smerge__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))
% Assm [h4s_enumerals_smergeu_u_outu_u_tupledu_u_primitive]: !_9. (!smerge__out__tupled cmp l lol m. happ (happ (happ (happ (happ _9 smerge__out__tupled) cmp) l) lol) m = h4/combin/I (happ smerge__out__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol)))) ==> (!_8. (!v4 smerge__out__tupled cmp l lol. happ (happ (happ (happ (happ _8 v4) smerge__out__tupled) cmp) l) lol = h4/option/option__CASE v4 (h4/combin/I (happ smerge__out__tupled (h4/pair/_2C cmp (h4/pair/_2C l lol)))) (happ (happ (happ (happ _9 smerge__out__tupled) cmp) l) lol)) ==> (!_7. (!smerge__out__tupled cmp l v4. happ (happ (happ (happ _7 smerge__out__tupled) cmp) l) v4 = happ (happ (happ (happ _8 v4) smerge__out__tupled) cmp) l) ==> (!_6. (!smerge__out__tupled cmp l v3. happ (happ (happ (happ _6 smerge__out__tupled) cmp) l) v3 = h4/list/list__CASE v3 (h4/combin/I l) (happ (happ (happ _7 smerge__out__tupled) cmp) l)) ==> (!_5. (!smerge__out__tupled cmp l. happ (happ (happ _5 smerge__out__tupled) cmp) l = happ (happ (happ _6 smerge__out__tupled) cmp) l) ==> (!_4. (!smerge__out__tupled cmp v1. happ (happ (happ _4 smerge__out__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 smerge__out__tupled) cmp)) ==> (!_3. (!smerge__out__tupled cmp. happ (happ _3 smerge__out__tupled) cmp = happ (happ _4 smerge__out__tupled) cmp) ==> (!_2. (!smerge__out__tupled a. happ (happ _2 smerge__out__tupled) a = h4/pair/pair__CASE a (happ _3 smerge__out__tupled)) ==> (!_1. (!smerge__out__tupled. happ _1 smerge__out__tupled = happ _2 smerge__out__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!lol l cmp. happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l lol))) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS h4/option/NONE lol)))) /\ (!lol m l cmp. happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/smerge cmp l m) lol))) (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS (happ h4/option/SOME m) lol))))) ==> h4/enumeral/smerge__out__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))
% Assm [h4s_enumerals_incru_u_smerge0u_c2]: !m lol l cmp. h4/enumeral/incr__smerge cmp l (h4/list/CONS (happ h4/option/SOME m) lol) = h4/list/CONS h4/option/NONE (h4/enumeral/incr__smerge cmp (h4/enumeral/smerge cmp l m) lol)
% Assm [h4s_enumerals_lolu_u_setu_u_primitive]: !_5. (!lol__set lol m. happ (happ (happ _5 lol__set) lol) m = h4/combin/I (h4/pred__set/UNION (h4/list/LIST__TO__SET m) (happ lol__set lol))) ==> (!_4. (!v lol__set lol. happ (happ (happ _4 v) lol__set) lol = h4/option/option__CASE v (h4/combin/I (happ lol__set lol)) (happ (happ _5 lol__set) lol)) ==> (!_3. (!lol__set v. happ (happ _3 lol__set) v = happ (happ _4 v) lol__set) ==> (!_2. (!lol__set a. happ (happ _2 lol__set) a = h4/list/list__CASE a (h4/combin/I h4/pred__set/EMPTY) (happ _3 lol__set)) ==> (!_1. (!lol__set. happ _1 lol__set = happ _2 lol__set) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!lol. happ (happ R lol) (h4/list/CONS h4/option/NONE lol)) /\ (!m lol. happ (happ R lol) (h4/list/CONS (happ h4/option/SOME m) lol))) ==> h4/enumeral/lol__set = h4/relation/WFREC (h4/min/_40 _0) _1)))))
% Assm [h4s_enumerals_OLu_u_sublistsu_u_tupledu_u_primitive]: !_7. (!OL__sublists__tupled cmp lol m. ?v. (v <=> h4/enumeral/OL cmp m /\ happ OL__sublists__tupled (h4/pair/_2C cmp lol)) /\ (happ (happ (happ (happ _7 OL__sublists__tupled) cmp) lol) m <=> h4/combin/I v)) ==> (!_6. (!v2 OL__sublists__tupled cmp lol. happ (happ (happ (happ _6 v2) OL__sublists__tupled) cmp) lol <=> h4/option/option__CASE v2 (h4/combin/I (happ OL__sublists__tupled (h4/pair/_2C cmp lol))) (happ (happ (happ _7 OL__sublists__tupled) cmp) lol)) ==> (!_5. (!OL__sublists__tupled cmp v2. happ (happ (happ _5 OL__sublists__tupled) cmp) v2 = happ (happ (happ _6 v2) OL__sublists__tupled) cmp) ==> (!_4. (!OL__sublists__tupled cmp v1. happ (happ (happ _4 OL__sublists__tupled) cmp) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 OL__sublists__tupled) cmp)) ==> (!_3. (!OL__sublists__tupled cmp. happ (happ _3 OL__sublists__tupled) cmp = happ (happ _4 OL__sublists__tupled) cmp) ==> (!_2. (!OL__sublists__tupled a. happ (happ _2 OL__sublists__tupled) a <=> h4/pair/pair__CASE a (happ _3 OL__sublists__tupled)) ==> (!_1. (!OL__sublists__tupled. happ _1 OL__sublists__tupled = happ _2 OL__sublists__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!lol cmp. happ (happ R (h4/pair/_2C cmp lol)) (h4/pair/_2C cmp (h4/list/CONS h4/option/NONE lol))) /\ (!m lol cmp. happ (happ R (h4/pair/_2C cmp lol)) (h4/pair/_2C cmp (h4/list/CONS (happ h4/option/SOME m) lol)))) ==> h4/enumeral/OL__sublists__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))
% Assm [h4s_enumerals_smergeu_u_out0u_c1]: !lol l cmp. h4/enumeral/smerge__out cmp l (h4/list/CONS h4/option/NONE lol) = h4/enumeral/smerge__out cmp l lol
% Assm [h4s_enumerals_incru_u_smerge0u_c1]: !lol l cmp. h4/enumeral/incr__smerge cmp l (h4/list/CONS h4/option/NONE lol) = h4/list/CONS (happ h4/option/SOME l) lol
% Assm [h4s_enumerals_lolu_u_set0u_c1]: !lol. happ h4/enumeral/lol__set (h4/list/CONS h4/option/NONE lol) = happ h4/enumeral/lol__set lol
% Assm [h4s_enumerals_OLu_u_sublists0u_c1]: !lol cmp. h4/enumeral/OL__sublists cmp (h4/list/CONS h4/option/NONE lol) <=> h4/enumeral/OL__sublists cmp lol
% Assm [h4s_strings_DESTu_u_STRINGu_u_defu_c0]: h4/string/DEST__STRING h4/list/NIL = h4/option/NONE
% Assm [h4s_enumerals_OLu_u_sublistsu_u_ind]: !P. (!cmp. happ (happ P cmp) h4/list/NIL) /\ (!cmp lol. happ (happ P cmp) lol ==> happ (happ P cmp) (h4/list/CONS h4/option/NONE lol)) /\ (!cmp m lol. happ (happ P cmp) lol ==> happ (happ P cmp) (h4/list/CONS (happ h4/option/SOME m) lol)) ==> (!v v1. happ (happ P v) v1)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_enumerals_smergeu_u_outu_u_ind]: !P. (!cmp l. happ (happ (happ P cmp) l) h4/list/NIL) /\ (!cmp l lol. happ (happ (happ P cmp) l) lol ==> happ (happ (happ P cmp) l) (h4/list/CONS h4/option/NONE lol)) /\ (!cmp l m lol. happ (happ (happ P cmp) (h4/enumeral/smerge cmp l m)) lol ==> happ (happ (happ P cmp) l) (h4/list/CONS (happ h4/option/SOME m) lol)) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
% Assm [h4s_enumerals_lolu_u_setu_u_ind]: !P. happ P h4/list/NIL /\ (!lol. happ P lol ==> happ P (h4/list/CONS h4/option/NONE lol)) /\ (!m lol. happ P lol ==> happ P (h4/list/CONS (happ h4/option/SOME m) lol)) ==> (!v. happ P v)
% Assm [h4s_enumerals_incru_u_smergeu_u_ind]: !P. (!cmp l. happ (happ (happ P cmp) l) h4/list/NIL) /\ (!cmp l lol. happ (happ (happ P cmp) l) (h4/list/CONS h4/option/NONE lol)) /\ (!cmp l m lol. happ (happ (happ P cmp) (h4/enumeral/smerge cmp l m)) lol ==> happ (happ (happ P cmp) l) (h4/list/CONS (happ h4/option/SOME m) lol)) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
% Assm [h4s_strings_EXTRACTu_u_defu_c0]: !s i. happ h4/string/EXTRACT (h4/pair/_2C s (h4/pair/_2C i h4/option/NONE)) = h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i (h4/arithmetic/_2D (h4/list/LENGTH s) i)))
% Assm [h4s_strings_DESTu_u_STRINGu_u_LEMSu_c0]: !s. h4/string/DEST__STRING s = h4/option/NONE <=> s = h4/list/NIL
% Assm [h4s_strings_EXTRACTu_u_ind]: !P. (!s i. happ P (h4/pair/_2C s (h4/pair/_2C i h4/option/NONE))) /\ (!s i n. happ P (h4/pair/_2C s (h4/pair/_2C i (happ h4/option/SOME n)))) ==> (!v v1 v2. happ P (h4/pair/_2C v (h4/pair/_2C v1 v2)))
% Assm [h4s_options_optionu_u_caseu_u_ID]: !x. h4/option/option__CASE x h4/option/NONE h4/option/SOME = x
% Assm [h4s_options_NONEu_u_DEF]: h4/option/NONE = h4/option/option__ABS (h4/sum/INR h4/one/one0)
% Assm [h4s_options_OPTIONu_u_GUARDu_u_COND]: !b. h4/option/OPTION__GUARD b = h4/bool/COND b (happ h4/option/SOME h4/one/one0) h4/option/NONE
% Assm [h4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_FLOOKUP]: !y x f. h4/finite__map/SUBMAP f (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) <=> h4/finite__map/FLOOKUP f x = h4/option/NONE \/ h4/finite__map/FLOOKUP f x = happ h4/option/SOME y
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_options_SOMEu_u_11]: !y x. happ h4/option/SOME x = happ h4/option/SOME y <=> x = y
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_enumerals_incru_u_smergeu_u_curried]: !x2 x1 x. h4/enumeral/incr__smerge x x1 x2 = happ h4/enumeral/incr__smerge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_strings_EXTRACTu_u_primitiveu_u_def]: !_7. (!s i n. happ (happ (happ _7 s) i) n = h4/combin/I (h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i n)))) ==> (!_6. (!s i v3. happ (happ (happ _6 s) i) v3 = h4/option/option__CASE v3 (h4/combin/I (h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i (h4/arithmetic/_2D (h4/list/LENGTH s) i))))) (happ (happ _7 s) i)) ==> (!_5. (!s i. happ (happ _5 s) i = happ (happ _6 s) i) ==> (!_4. (!s v1. happ (happ _4 s) v1 = h4/pair/pair__CASE v1 (happ _5 s)) ==> (!_3. (!s. happ _3 s = happ _4 s) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!EXTRACT. happ _1 EXTRACT = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/string/EXTRACT = h4/relation/WFREC (h4/min/_40 _0) _1)))))))
% Assm [h4s_enumerals_smergeu_u_outu_u_curried]: !x2 x1 x. h4/enumeral/smerge__out x x1 x2 = happ h4/enumeral/smerge__out__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_enumerals_OLu_u_sublistsu_u_curried]: !x1 x. h4/enumeral/OL__sublists x x1 <=> happ h4/enumeral/OL__sublists__tupled (h4/pair/_2C x x1)
% Assm [h4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_EQN]: !y x f. h4/finite__map/SUBMAP f (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) <=> ~h4/bool/IN x (h4/finite__map/FDOM f) \/ h4/finite__map/FAPPLY f x = y /\ h4/bool/IN x (h4/finite__map/FDOM f)
% 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_bools_CONJu_u_COMM]: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c0]: !x P. h4/bool/COND P (happ h4/option/SOME x) h4/option/NONE = h4/option/NONE <=> ~P
% Assm [h4s_options_IFu_u_EQUALSu_u_OPTIONu_c2]: !y x P. h4/bool/COND P (happ h4/option/SOME x) h4/option/NONE = happ h4/option/SOME y <=> P /\ x = y
% Assm [h4s_markers_ACu_u_DEF]: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% 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_options_OPTIONu_u_GUARDu_u_defu_c1]: h4/option/OPTION__GUARD F = h4/option/NONE
% Assm [h4s_options_OPTIONu_u_GUARDu_u_defu_c0]: h4/option/OPTION__GUARD T = happ h4/option/SOME h4/one/one0
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_strings_DESTu_u_STRINGu_u_defu_c1]: !rst c. h4/string/DEST__STRING (h4/list/CONS c rst) = happ h4/option/SOME (h4/pair/_2C c rst)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_lists_NOTu_u_NILu_u_CONS]: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_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_options_NOTu_u_NONEu_u_SOME]: !x. ~(h4/option/NONE = happ h4/option/SOME x)
% Goal: !l f. h4/fmapal/optry__list f (h4/list/CONS h4/option/NONE l) = h4/fmapal/optry__list f l
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q1310110,TV_Q1310106]: ![V_f, V_g]: (![V_x]: s(TV_Q1310106,happ(s(t_fun(TV_Q1310110,TV_Q1310106),V_f),s(TV_Q1310110,V_x))) = s(TV_Q1310106,happ(s(t_fun(TV_Q1310110,TV_Q1310106),V_g),s(TV_Q1310110,V_x))) => s(t_fun(TV_Q1310110,TV_Q1310106),V_f) = s(t_fun(TV_Q1310110,TV_Q1310106),V_g))).
fof(ah4s_fmapals_optryu_u_listu_u_curried, axiom, ![TV_u_27g,TV_u_27z]: ![V_x1, V_x]: s(t_h4s_options_option(TV_u_27g),h4s_fmapals_optryu_u_list(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_x),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_x1))) = s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),h4s_fmapals_optryu_u_listu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_x),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_x1)))))).
fof(ah4s_fmapals_optryu_u_listu_u_tupledu_u_primitive, axiom, ![TV_u_27z,TV_u_27g]: ![V_uu_7]: (![V_optryu_u_listu_u_tupled, V_f, V_l, V_z]: s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))),s(TV_u_27z,V_z))) = s(t_h4s_options_option(TV_u_27g),h4s_combins_i(s(t_h4s_options_option(TV_u_27g),h4s_fmapals_optry(s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(TV_u_27z,V_z))),s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))))))) => ![V_uu_6]: (![V_v2, V_optryu_u_listu_u_tupled, V_f, V_l]: s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))))),V_uu_6),s(t_h4s_options_option(TV_u_27z),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))) = s(t_h4s_options_option(TV_u_27g),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27z),V_v2),s(t_h4s_options_option(TV_u_27g),h4s_combins_i(s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))) => ![V_uu_5]: (![V_optryu_u_listu_u_tupled, V_f, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_options_option(TV_u_27z),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))))),V_uu_6),s(t_h4s_options_option(TV_u_27z),V_v2))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))) => ![V_uu_4]: (![V_optryu_u_listu_u_tupled, V_f, V_v1]: s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_v1))) = s(t_h4s_options_option(TV_u_27g),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_v1),s(t_h4s_options_option(TV_u_27g),h4s_combins_i(s(t_h4s_options_option(TV_u_27g),h4s_options_none))),s(t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_options_option(TV_u_27z),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))))) => ![V_uu_3]: (![V_optryu_u_listu_u_tupled, V_f]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))) => ![V_uu_2]: (![V_optryu_u_listu_u_tupled, V_a]: s(t_h4s_options_option(TV_u_27g),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),V_a))) = s(t_h4s_options_option(TV_u_27g),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),V_a),s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_h4s_options_option(TV_u_27g)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))))) => ![V_uu_1]: (![V_optryu_u_listu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),V_optryu_u_listu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),V_R)))) & (![V_l, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_cons(s(t_h4s_options_option(TV_u_27z),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l)))))))) & ![V_z, V_l, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))),s(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),h4s_pairs_u_2c(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_cons(s(t_h4s_options_option(TV_u_27z),happ(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27z)),h4s_options_some),s(TV_u_27z,V_z))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),h4s_fmapals_optryu_u_listu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_h4s_lists_list(t_h4s_options_option(TV_u_27z))),t_h4s_options_option(TV_u_27g))),V_uu_1)))))))))))).
fof(ah4s_fmapals_optryu_u_listu_u_ind, axiom, ![TV_u_27g,TV_u_27z]: ![V_P]: ((![V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_nil)))) & (![V_f, V_l]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_cons(s(t_h4s_options_option(TV_u_27z),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))))) & ![V_f, V_z, V_l]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_cons(s(t_h4s_options_option(TV_u_27z),happ(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27z)),h4s_options_some),s(TV_u_27z,V_z))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool),happ(s(t_fun(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),t_fun(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),t_bool)),V_P),s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_v))),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_v1)))))).
fof(ah4s_options_optionu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_e]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(TV_u_27b,V_e) & ![V_x]: s(TV_u_27b,happ(s(t_fun(t_h4s_options_option(TV_u_27a),TV_u_27b),V_fn),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,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))).
fof(ah4s_fmapals_optryu_u_list0u_c0, axiom, ![TV_u_27z,TV_u_27g]: ![V_f]: s(t_h4s_options_option(TV_u_27g),h4s_fmapals_optryu_u_list(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_nil))) = s(t_h4s_options_option(TV_u_27g),h4s_options_none)).
fof(ah4s_options_OPTIONu_u_BINDu_u_defu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_f]: s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_bind(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_x))),s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27a)),V_f))) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27a)),V_f),s(TV_u_27b,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,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_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))))).
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_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_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_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_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_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_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_basicSizes_optionu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_f]: s(t_h4s_nums_num,h4s_basicsizes_optionu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),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_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_x)))))).
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_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_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_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_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_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_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_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_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_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_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_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_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_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_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> s(t_bool,V_t) = s(t_bool,f0))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_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_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,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_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_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
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_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_basicSizes_optionu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_nums_num,h4s_basicsizes_optionu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_h4s_nums_num,h4s_nums_0)).
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,f0)).
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_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_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_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_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_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_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_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_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_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_lists_listu_u_nchotomy, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) | ?[V_h, V_t]: s(t_h4s_lists_list(TV_u_27a),V_l) = 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))))).
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,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_options_optionu_u_caseu_u_defu_c1, 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_caseu_u_defu_c0, 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_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_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_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_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_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),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,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
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_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_enumerals_incru_u_smergeu_u_tupledu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_9]: (![V_incru_u_smergeu_u_tupled, V_cmp, V_l, V_lol, V_m]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_combins_i(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))))) => ![V_uu_8]: (![V_v4, V_incru_u_smergeu_u_tupled, V_cmp, V_l, V_lol]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),happ(s(t_fun(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_8),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_combins_i(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) => ![V_uu_7]: (![V_incru_u_smergeu_u_tupled, V_cmp, V_l, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),happ(s(t_fun(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_8),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) => ![V_uu_6]: (![V_incru_u_smergeu_u_tupled, V_cmp, V_l, V_v3]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v3))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v3),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_combins_i(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_nil))))),s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))))) => ![V_uu_5]: (![V_incru_u_smergeu_u_tupled, V_cmp, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) => ![V_uu_4]: (![V_incru_u_smergeu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_v1))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_v1),s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_incru_u_smergeu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_incru_u_smergeu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_a))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))))) => ![V_uu_1]: (![V_incru_u_smergeu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_incru_u_smergeu_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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_bool)),V_R)))) & ![V_lol, V_m, 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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_enumerals_incru_u_smergeu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_uu_1)))))))))))))).
fof(ah4s_enumerals_smergeu_u_outu_u_tupledu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_9]: (![V_smergeu_u_outu_u_tupled, V_cmp, V_l, V_lol, V_m]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => ![V_uu_8]: (![V_v4, V_smergeu_u_outu_u_tupled, V_cmp, V_l, V_lol]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))))),V_uu_8),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))) = s(t_h4s_lists_list(TV_u_27a),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) => ![V_uu_7]: (![V_smergeu_u_outu_u_tupled, V_cmp, V_l, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))))),V_uu_8),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) => ![V_uu_6]: (![V_smergeu_u_outu_u_tupled, V_cmp, V_l, V_v3]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v3))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v3),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))))) => ![V_uu_5]: (![V_smergeu_u_outu_u_tupled, V_cmp, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_l))) => ![V_uu_4]: (![V_smergeu_u_outu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_v1))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_v1),s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_smergeu_u_outu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_smergeu_u_outu_u_tupled, V_a]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_a))) = s(t_h4s_lists_list(TV_u_27a),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_h4s_lists_list(TV_u_27a)))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))))) => ![V_uu_1]: (![V_smergeu_u_outu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_outu_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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_bool)),V_R)))) & (![V_lol, 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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))))))) & ![V_lol, V_m, 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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),h4s_enumerals_smergeu_u_outu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a))),V_uu_1)))))))))))))).
fof(ah4s_enumerals_incru_u_smerge0u_c2, axiom, ![TV_u_27a]: ![V_m, V_lol, V_l, V_cmp]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_enumerals_incru_u_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_enumerals_incru_u_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))).
fof(ah4s_enumerals_lolu_u_setu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_5]: (![V_lolu_u_set, V_lol, V_m]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool)))),V_uu_5),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_fun(TV_u_27a,t_bool),h4s_combins_i(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(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))),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))) => ![V_uu_4]: (![V_v, V_lolu_u_set, V_lol]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)))),V_uu_4),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v))),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))) = s(t_fun(TV_u_27a,t_bool),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v),s(t_fun(TV_u_27a,t_bool),h4s_combins_i(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))),s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_bool)))),V_uu_5),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) => ![V_uu_3]: (![V_lolu_u_set, V_v]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)))),V_uu_3),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)))),V_uu_4),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v))),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))) => ![V_uu_2]: (![V_lolu_u_set, V_a]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_a))) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_a),s(t_fun(TV_u_27a,t_bool),h4s_combins_i(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)))),V_uu_3),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))))) => ![V_uu_1]: (![V_lolu_u_set]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),V_lolu_u_set))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) & (![V_lol]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))) & ![V_m, V_lol]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),h4s_enumerals_lolu_u_set) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),h4s_relations_wfrec(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool))),V_uu_1)))))))))).
fof(ah4s_enumerals_OLu_u_sublistsu_u_tupledu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_7]: (![V_OLu_u_sublistsu_u_tupled, V_cmp, V_lol, V_m]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (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,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))))) & 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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_6]: (![V_v2, V_OLu_u_sublistsu_u_tupled, V_cmp, V_lol]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool))),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)))),V_uu_6),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))) = s(t_bool,h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v2),s(t_bool,h4s_combins_i(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))),s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_lists_list(TV_u_27a),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) => ![V_uu_5]: (![V_OLu_u_sublistsu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool))),happ(s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)))),V_uu_6),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_OLu_u_sublistsu_u_tupled, V_cmp, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v1))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v1),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_OLu_u_sublistsu_u_tupled, V_cmp]: s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_OLu_u_sublistsu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_a))) = 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_options_option(t_h4s_lists_list(TV_u_27a)))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))))) => ![V_uu_1]: (![V_OLu_u_sublistsu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),V_OLu_u_sublistsu_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_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool)),V_R)))) & (![V_lol, 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_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))))) & ![V_m, V_lol, 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_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),h4s_enumerals_olu_u_sublistsu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool)),V_uu_1)))))))))))).
fof(ah4s_enumerals_smergeu_u_out0u_c1, axiom, ![TV_u_27a]: ![V_lol, V_l, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smergeu_u_out(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) = s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smergeu_u_out(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))).
fof(ah4s_enumerals_incru_u_smerge0u_c1, axiom, ![TV_u_27a]: ![V_lol, V_l, V_cmp]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_enumerals_incru_u_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))).
fof(ah4s_enumerals_lolu_u_set0u_c1, axiom, ![TV_u_27a]: ![V_lol]: s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),h4s_enumerals_lolu_u_set),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) = s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_fun(TV_u_27a,t_bool)),h4s_enumerals_lolu_u_set),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))).
fof(ah4s_enumerals_OLu_u_sublists0u_c1, axiom, ![TV_u_27a]: ![V_lol, V_cmp]: s(t_bool,h4s_enumerals_olu_u_sublists(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))) = s(t_bool,h4s_enumerals_olu_u_sublists(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))).
fof(ah4s_strings_DESTu_u_STRINGu_u_defu_c0, axiom, s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_options_none)).
fof(ah4s_enumerals_OLu_u_sublistsu_u_ind, axiom, ![TV_u_27a]: ![V_P]: ((![V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_nil)))) & (![V_cmp, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))) & ![V_cmp, V_m, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(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_options_option(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_options_option(t_h4s_lists_list(TV_u_27a))),V_v1)))))).
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_enumerals_smergeu_u_outu_u_ind, axiom, ![TV_u_27a]: ![V_P]: ((![V_cmp, V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_nil)))) & (![V_cmp, V_l, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))) & ![V_cmp, V_l, V_m, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_v1))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v2)))))).
fof(ah4s_enumerals_lolu_u_setu_u_ind, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_nil)))) & (![V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))) & ![V_m, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => ![V_v]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),V_P),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v)))))).
fof(ah4s_enumerals_incru_u_smergeu_u_ind, axiom, ![TV_u_27a]: ![V_P]: ((![V_cmp, V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_nil)))) & (![V_cmp, V_l, V_lol]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))))) & ![V_cmp, V_l, V_m, V_lol]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),h4s_enumerals_smerge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol)))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_lists_cons(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_options_some),s(t_h4s_lists_list(TV_u_27a),V_m))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_lol))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),V_v1))),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_v2)))))).
fof(ah4s_strings_EXTRACTu_u_defu_c0, axiom, ![V_s, V_i]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_extract),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_options_option(t_h4s_nums_num),h4s_options_none))))))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_substring(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i)))))))))).
fof(ah4s_strings_DESTu_u_STRINGu_u_LEMSu_c0, axiom, ![V_s]: (s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_options_none) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_s) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))).
fof(ah4s_strings_EXTRACTu_u_ind, axiom, ![V_P]: ((![V_s, V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_options_option(t_h4s_nums_num),h4s_options_none)))))))) & ![V_s, V_i, V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_options_option(t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_options_some),s(t_h4s_nums_num,V_n))))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_v),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_v1),s(t_h4s_options_option(t_h4s_nums_num),V_v2)))))))))).
fof(ah4s_options_optionu_u_caseu_u_ID, 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_NONEu_u_DEF, axiom, ![TV_u_27a]: s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),h4s_options_optionu_u_abs(s(t_h4s_sums_sum(TV_u_27a,t_h4s_ones_one),h4s_sums_inr(s(t_h4s_ones_one,h4s_ones_one0)))))).
fof(ah4s_options_OPTIONu_u_GUARDu_u_COND, axiom, ![V_b]: s(t_h4s_options_option(t_h4s_ones_one),h4s_options_optionu_u_guard(s(t_bool,V_b))) = s(t_h4s_options_option(t_h4s_ones_one),h4s_bools_cond(s(t_bool,V_b),s(t_h4s_options_option(t_h4s_ones_one),happ(s(t_fun(t_h4s_ones_one,t_h4s_options_option(t_h4s_ones_one)),h4s_options_some),s(t_h4s_ones_one,h4s_ones_one0))),s(t_h4s_options_option(t_h4s_ones_one),h4s_options_none)))).
fof(ah4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_FLOOKUP, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: (p(s(t_bool,h4s_finiteu_u_maps_submap(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),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)))))))) <=> (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_options_none) | 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),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),h4s_options_some),s(TV_u_27b,V_y)))))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f0)).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_options_SOMEu_u_11, 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_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_enumerals_incru_u_smergeu_u_curried, axiom, ![TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),h4s_enumerals_incru_u_smerge(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_x2))) = s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_enumerals_incru_u_smergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_x2)))))))).
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_strings_EXTRACTu_u_primitiveu_u_def, axiom, ![V_uu_7]: (![V_s, V_i, V_n]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char)))),V_uu_7),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_n))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_combins_i(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_substring(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))))) => ![V_uu_6]: (![V_s, V_i, V_v3]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)))),V_uu_6),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))),s(t_h4s_options_option(t_h4s_nums_num),V_v3))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_nums_num),V_v3),s(t_h4s_lists_list(t_h4s_strings_char),h4s_combins_i(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_substring(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))))))))))),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_strings_char)))),V_uu_7),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))))) => ![V_uu_5]: (![V_s, V_i]: s(t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)))),V_uu_5),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))) = s(t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)))),V_uu_6),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_i))) => ![V_uu_4]: (![V_s, V_v1]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char))),V_uu_4),s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),V_v1))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),V_v1),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_nums_num,t_fun(t_h4s_options_option(t_h4s_nums_num),t_h4s_lists_list(t_h4s_strings_char)))),V_uu_5),s(t_h4s_lists_list(t_h4s_strings_char),V_s))))) => ![V_uu_3]: (![V_s]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char))),V_uu_3),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char))),V_uu_4),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) => ![V_uu_2]: (![V_a]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),V_a))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),V_a),s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),t_h4s_lists_list(t_h4s_strings_char))),V_uu_3))) => ![V_uu_1]: (![V_EXTRACT]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),V_EXTRACT))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_extract) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num))),t_h4s_lists_list(t_h4s_strings_char))),V_uu_1)))))))))))).
fof(ah4s_enumerals_smergeu_u_outu_u_curried, axiom, ![TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_smergeu_u_out(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_x2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),t_h4s_lists_list(TV_u_27a)),h4s_enumerals_smergeu_u_outu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(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(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_x1),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_x2)))))))).
fof(ah4s_enumerals_OLu_u_sublistsu_u_curried, axiom, ![TV_u_27a]: ![V_x1, V_x]: s(t_bool,h4s_enumerals_olu_u_sublists(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),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_options_option(t_h4s_lists_list(TV_u_27a)))),t_bool),h4s_enumerals_olu_u_sublistsu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),V_x1)))))).
fof(ah4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_EQN, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: (p(s(t_bool,h4s_finiteu_u_maps_submap(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),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)))))))) <=> (~ (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,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)))))))))).
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_bools_CONJu_u_COMM, 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))))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0, axiom, ![TV_u_27a]: ![V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_P),s(t_h4s_options_option(TV_u_27a),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))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) <=> ~ (p(s(t_bool,V_P))))).
fof(ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2, axiom, ![TV_u_27a]: ![V_y, V_x, V_P]: (s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_P),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))) = 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))) <=> (p(s(t_bool,V_P)) & s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_markers_ACu_u_DEF, axiom, ![V_b2, V_b1]: (p(s(t_bool,h4s_markers_ac(s(t_bool,V_b1),s(t_bool,V_b2)))) <=> (p(s(t_bool,V_b1)) & p(s(t_bool,V_b2))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_options_OPTIONu_u_GUARDu_u_defu_c1, axiom, s(t_h4s_options_option(t_h4s_ones_one),h4s_options_optionu_u_guard(s(t_bool,f0))) = s(t_h4s_options_option(t_h4s_ones_one),h4s_options_none)).
fof(ah4s_options_OPTIONu_u_GUARDu_u_defu_c0, axiom, s(t_h4s_options_option(t_h4s_ones_one),h4s_options_optionu_u_guard(s(t_bool,t))) = s(t_h4s_options_option(t_h4s_ones_one),happ(s(t_fun(t_h4s_ones_one,t_h4s_options_option(t_h4s_ones_one)),h4s_options_some),s(t_h4s_ones_one,h4s_ones_one0)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_strings_DESTu_u_STRINGu_u_defu_c1, axiom, ![V_rst, V_c]: s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),V_rst))))) = s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)))),h4s_options_some),s(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),V_rst)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f0) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_NOTu_u_NILu_u_CONS, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = 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))))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_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_options_NOTu_u_NONEu_u_SOME, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some),s(TV_u_27a,V_x))))).
fof(ch4s_fmapals_optryu_u_list0u_c1, conjecture, ![TV_u_27g,TV_u_27z]: ![V_l, V_f]: s(t_h4s_options_option(TV_u_27g),h4s_fmapals_optryu_u_list(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),h4s_lists_cons(s(t_h4s_options_option(TV_u_27z),h4s_options_none),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l))))) = s(t_h4s_options_option(TV_u_27g),h4s_fmapals_optryu_u_list(s(t_fun(TV_u_27z,t_h4s_options_option(TV_u_27g)),V_f),s(t_h4s_lists_list(t_h4s_options_option(TV_u_27z)),V_l)))).
