%   ORIGINAL: h4/fmapal/diff__merge__ind
% 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/inter__merge__ind: !P. (!cmp. P cmp h4/list/NIL h4/list/NIL) /\ (!cmp a b l. P cmp (h4/list/CONS (h4/pair/_2C a b) l) h4/list/NIL) /\ (!cmp y m. P cmp h4/list/NIL (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> P cmp l m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> P cmp l (h4/list/CONS y m)) ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)) ==> (!v v1 v2. P v v1 v2)
% Assm: h4/fmapal/inter__merge__tupled__primitive: h4/fmapal/inter__merge__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> R (h4/pair/_2C cmp (h4/pair/_2C l m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))))) (\inter__merge__tupled a_27. h4/pair/pair__CASE a_27 (\cmp v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (\v4 l. h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (\y m. h4/pair/pair__CASE v4 (\a b. h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/list/CONS (h4/pair/_2C a b) (inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m)))) (inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))))))))
% Assm: h4/fmapal/diff__merge__tupled__primitive: h4/fmapal/diff__merge__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> R (h4/pair/_2C cmp (h4/pair/_2C l m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))))) (\diff__merge__tupled a_27. h4/pair/pair__CASE a_27 (\cmp v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (\v4 l. h4/pair/pair__CASE v4 (\a b. h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (h4/pair/_2C a b) l)) (\y m. h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/list/CONS (h4/pair/_2C a b) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))))) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m))) (diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))))))))
% Assm: h4/fmapal/inter__merge0_c3: !y m l cmp b a. h4/fmapal/inter__merge cmp (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m) = h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/fmapal/inter__merge cmp l (h4/list/CONS y m)) (h4/list/CONS (h4/pair/_2C a b) (h4/fmapal/inter__merge cmp l m)) (h4/fmapal/inter__merge cmp (h4/list/CONS (h4/pair/_2C a b) l) m)
% Assm: h4/fmapal/ORL__tupled__primitive: h4/fmapal/ORL__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b a l cmp. R (h4/pair/_2C cmp l) (h4/pair/_2C cmp (h4/list/CONS (h4/pair/_2C a b) l))))) (\ORL__tupled a_27. h4/pair/pair__CASE a_27 (\cmp v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 l. h4/pair/pair__CASE v2 (\a b. h4/combin/I (ORL__tupled (h4/pair/_2C cmp l) /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS))))))
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/TRUTH: T
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% 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/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/fmapal/ORL0_c1: !l cmp b a. h4/fmapal/ORL cmp (h4/list/CONS (h4/pair/_2C a b) l) <=> h4/fmapal/ORL cmp l /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% 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/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/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__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% 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/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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/numeral/numeral__add_c1: !n. h4/numeral/iZ (h4/arithmetic/_2B n h4/arithmetic/ZERO) = n
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/arithmetic/LESS__MONO__ADD__EQ: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm: h4/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/LEFT__OR__EXISTS__THM: !Q P. (?x. P x) \/ Q <=> (?x. P x \/ Q)
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/fmapal/assocv__tupled__primitive: h4/fmapal/assocv__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y l x a. ~(a = x) ==> R (h4/pair/_2C l a) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C x y) l) a)))) (\assocv__tupled a_27. h4/pair/pair__CASE a_27 (\v a. h4/list/list__CASE v (h4/combin/I h4/option/NONE) (\v2 l. h4/pair/pair__CASE v2 (\x y. h4/combin/I (h4/bool/COND (a = x) (h4/option/SOME y) (assocv__tupled (h4/pair/_2C l a)))))))
% Assm: h4/fmapal/assocv__ind: !P. (!a. P h4/list/NIL a) /\ (!x y l a. (~(a = x) ==> P l a) ==> P (h4/list/CONS (h4/pair/_2C x y) l) a) ==> (!v v1. P v v1)
% Assm: h4/fmapal/assocv0_c1: !y x l a. h4/fmapal/assocv (h4/list/CONS (h4/pair/_2C x y) l) a = h4/bool/COND (a = x) (h4/option/SOME y) (h4/fmapal/assocv l a)
% Assm: h4/fmapal/bt__to__orl__ub__tupled__primitive: h4/fmapal/bt__to__orl__ub__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!r y l ub x cmp. ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> R (h4/pair/_2C cmp (h4/pair/_2C l ub)) (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub))) /\ (!r y l ub x cmp. h4/toto/apto cmp x ub = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C l x)) (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub))))) (\bt__to__orl__ub__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\v2 ub. h4/enumeral/bt__CASE v2 (h4/combin/I h4/list/NIL) (\l v5 r. h4/pair/pair__CASE v5 (\x y. h4/combin/I (h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (bt__to__orl__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C l x))) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (bt__to__orl__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C l ub)))))))))
% Assm: h4/fmapal/bt__to__orl__lb__ub__tupled__primitive: h4/fmapal/bt__to__orl__lb__ub__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y l ub r x lb cmp. ~(h4/toto/apto cmp lb x = h4/toto/LESS) ==> R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C r ub))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!r y l ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l ub))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!r y l ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l x))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!y l r ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C x (h4/pair/_2C r ub))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))))) (\bt__to__orl__lb__ub__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\lb v3. h4/pair/pair__CASE v3 (\v4 ub. h4/enumeral/bt__CASE v4 (h4/combin/I h4/list/NIL) (\l v7 r. h4/pair/pair__CASE v7 (\x y. h4/combin/I (h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l x)))) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C x (h4/pair/_2C r ub))))) (bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l ub))))) (bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C r ub)))))))))))
% Assm: h4/fmapal/bt__to__fmap__tupled__primitive: h4/fmapal/bt__to__fmap__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!r v x l cmp. R (h4/pair/_2C cmp l) (h4/pair/_2C cmp (h4/enumeral/node l (h4/pair/_2C x v) r))) /\ (!v x l r cmp. R (h4/pair/_2C cmp r) (h4/pair/_2C cmp (h4/enumeral/node l (h4/pair/_2C x v) r))))) (\bt__to__fmap__tupled a. h4/pair/pair__CASE a (\cmp v2. h4/enumeral/bt__CASE v2 (h4/combin/I h4/finite__map/FEMPTY) (\l v4 r. h4/pair/pair__CASE v4 (\x v. h4/combin/I (h4/finite__map/FUNION (h4/finite__map/FUNION (h4/finite__map/DRESTRICT (bt__to__fmap__tupled (h4/pair/_2C cmp l)) (h4/pred__set/GSPEC (\y. h4/pair/_2C y (h4/toto/apto cmp y x = h4/toto/LESS)))) (h4/finite__map/FUPDATE h4/finite__map/FEMPTY (h4/pair/_2C x v))) (h4/finite__map/DRESTRICT (bt__to__fmap__tupled (h4/pair/_2C cmp r)) (h4/pred__set/GSPEC (\z. h4/pair/_2C z (h4/toto/apto cmp x z = h4/toto/LESS)))))))))
% Assm: h4/fmapal/bt__to__orl__ub0_c1: !y x ub r l cmp. h4/fmapal/bt__to__orl__ub cmp (h4/enumeral/node l (h4/pair/_2C x y) r) ub = h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (h4/fmapal/bt__to__orl__ub cmp l x) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (h4/fmapal/bt__to__orl__ub cmp l ub)
% Assm: h4/fmapal/bt__to__orl__lb__ub0_c1: !y x ub r lb l cmp. h4/fmapal/bt__to__orl__lb__ub cmp lb (h4/enumeral/node l (h4/pair/_2C x y) r) ub = h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (h4/fmapal/bt__to__orl__lb__ub cmp lb l x) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (h4/fmapal/bt__to__orl__lb__ub cmp lb l ub)) (h4/fmapal/bt__to__orl__lb__ub cmp lb r ub)
% Assm: h4/fmapal/bt__to__fmap_c1: !x v r l cmp. h4/fmapal/FMAPAL cmp (h4/enumeral/node l (h4/pair/_2C x v) r) = h4/finite__map/FUNION (h4/finite__map/FUNION (h4/finite__map/DRESTRICT (h4/fmapal/FMAPAL cmp l) (h4/pred__set/GSPEC (\y. h4/pair/_2C y (h4/toto/apto cmp y x = h4/toto/LESS)))) (h4/finite__map/FUPDATE h4/finite__map/FEMPTY (h4/pair/_2C x v))) (h4/finite__map/DRESTRICT (h4/fmapal/FMAPAL cmp r) (h4/pred__set/GSPEC (\z. h4/pair/_2C z (h4/toto/apto cmp x z = h4/toto/LESS))))
% Assm: h4/fmapal/bt__to__orl__ub__ind: !P. (!cmp ub. P cmp h4/enumeral/nt ub) /\ (!cmp l x y r ub. (~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> P cmp l ub) /\ (h4/toto/apto cmp x ub = h4/toto/LESS ==> P cmp l x) ==> P cmp (h4/enumeral/node l (h4/pair/_2C x y) r) ub) ==> (!v v1 v2. P v v1 v2)
% Assm: h4/fmapal/bt__to__orl__lb__ub__ind: !P. (!cmp lb ub. P cmp lb h4/enumeral/nt ub) /\ (!cmp lb l x y r ub. (~(h4/toto/apto cmp lb x = h4/toto/LESS) ==> P cmp lb r ub) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> P cmp lb l ub) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> P cmp lb l x) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> P cmp x r ub) ==> P cmp lb (h4/enumeral/node l (h4/pair/_2C x y) r) ub) ==> (!v v1 v2 v3. P v v1 v2 v3)
% Assm: h4/toto/aplextoto: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/enumeral/bt__size__def_c1: !f a2 a1 a0. h4/enumeral/bt__size f (h4/enumeral/node a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (f a1) (h4/enumeral/bt__size f a2)))
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/enumeral/bt__case__def_c1: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = f a0 a1 a2
% Assm: h4/enumeral/bt__case__def_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/fmapal/ORL__curried: !x1 x. h4/fmapal/ORL x x1 <=> h4/fmapal/ORL__tupled (h4/pair/_2C x x1)
% Assm: h4/fmapal/inter__merge__curried: !x2 x1 x. h4/fmapal/inter__merge x x1 x2 = h4/fmapal/inter__merge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/toto/cpn__case__cong: !v2_27 v2 v1_27 v1 v0_27 v0 M_27 M. M = M_27 /\ (M_27 = h4/toto/LESS ==> v0 = v0_27) /\ (M_27 = h4/toto/EQUAL ==> v1 = v1_27) /\ (M_27 = h4/toto/GREATER ==> v2 = v2_27) ==> h4/toto/cpn__CASE M v0 v1 v2 = h4/toto/cpn__CASE M_27 v0_27 v1_27 v2_27
% Assm: h4/enumeral/bt__nchotomy: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = h4/enumeral/node b a b0)
% Assm: h4/fmapal/assocv__curried: !x1 x. h4/fmapal/assocv x x1 = h4/fmapal/assocv__tupled (h4/pair/_2C x x1)
% Assm: h4/fmapal/bt__to__orl__ub__curried: !x2 x1 x. h4/fmapal/bt__to__orl__ub x x1 x2 = h4/fmapal/bt__to__orl__ub__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/fmapal/bt__to__orl__lb__ub__curried: !x3 x2 x1 x. h4/fmapal/bt__to__orl__lb__ub x x1 x2 x3 = h4/fmapal/bt__to__orl__lb__ub__tupled (h4/pair/_2C x (h4/pair/_2C x1 (h4/pair/_2C x2 x3)))
% Assm: h4/fmapal/bt__to__fmap__curried: !x1 x. h4/fmapal/FMAPAL x x1 = h4/fmapal/bt__to__fmap__tupled (h4/pair/_2C x x1)
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c20: !n. h4/prim__rec/_3C n h4/num/0 <=> F
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/arithmetic/SUB__LEFT__EQ: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/arithmetic/SUB__LEFT__LESS: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% Goal: !P. (!cmp. P cmp h4/list/NIL h4/list/NIL) /\ (!cmp a b l. P cmp (h4/list/CONS (h4/pair/_2C a b) l) h4/list/NIL) /\ (!cmp y m. P cmp h4/list/NIL (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> P cmp l m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> P cmp l (h4/list/CONS y m)) ==> P cmp (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)) ==> (!v v1 v2. P v v1 v2)
%   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_interu_u_mergeu_u_ind]: !P. (!cmp. happ (happ (happ P cmp) h4/list/NIL) h4/list/NIL) /\ (!cmp a b l. happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) h4/list/NIL) /\ (!cmp y m. happ (happ (happ P cmp) h4/list/NIL) (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ (happ P cmp) l) m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ (happ P cmp) l) (h4/list/CONS y m)) ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) (h4/list/CONS y m)) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
% Assm [h4s_fmapals_interu_u_mergeu_u_tupledu_u_primitive]: !_12. (!y inter__merge__tupled cmp a l m b. happ (happ (happ (happ (happ (happ (happ _12 y) inter__merge__tupled) cmp) a) l) m) b = h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (happ inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/list/CONS (h4/pair/_2C a b) (happ inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m)))) (happ inter__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))) ==> (!_11. (!y inter__merge__tupled cmp l m a. happ (happ (happ (happ (happ (happ _11 y) inter__merge__tupled) cmp) l) m) a = happ (happ (happ (happ (happ (happ _12 y) inter__merge__tupled) cmp) a) l) m) ==> (!_10. (!v4 y inter__merge__tupled cmp l m. happ (happ (happ (happ (happ (happ _10 v4) y) inter__merge__tupled) cmp) l) m = h4/pair/pair__CASE v4 (happ (happ (happ (happ (happ _11 y) inter__merge__tupled) cmp) l) m)) ==> (!_9. (!v4 inter__merge__tupled cmp l y. happ (happ (happ (happ (happ _9 v4) inter__merge__tupled) cmp) l) y = happ (happ (happ (happ (happ _10 v4) y) inter__merge__tupled) cmp) l) ==> (!_8. (!v3 v4 inter__merge__tupled cmp l. happ (happ (happ (happ (happ _8 v3) v4) inter__merge__tupled) cmp) l = h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (happ (happ (happ (happ _9 v4) inter__merge__tupled) cmp) l)) ==> (!_7. (!v3 inter__merge__tupled cmp v4. happ (happ (happ (happ _7 v3) inter__merge__tupled) cmp) v4 = happ (happ (happ (happ _8 v3) v4) inter__merge__tupled) cmp) ==> (!_6. (!v2 inter__merge__tupled cmp v3. happ (happ (happ (happ _6 v2) inter__merge__tupled) cmp) v3 = h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (happ (happ (happ _7 v3) inter__merge__tupled) cmp)) ==> (!_5. (!inter__merge__tupled cmp v2. happ (happ (happ _5 inter__merge__tupled) cmp) v2 = happ (happ (happ _6 v2) inter__merge__tupled) cmp) ==> (!_4. (!inter__merge__tupled cmp v1. happ (happ (happ _4 inter__merge__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 inter__merge__tupled) cmp)) ==> (!_3. (!inter__merge__tupled cmp. happ (happ _3 inter__merge__tupled) cmp = happ (happ _4 inter__merge__tupled) cmp) ==> (!_2. (!inter__merge__tupled a_27. happ (happ _2 inter__merge__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 inter__merge__tupled)) ==> (!_1. (!inter__merge__tupled. happ _1 inter__merge__tupled = happ _2 inter__merge__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m))))) ==> h4/fmapal/inter__merge__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_fmapals_diffu_u_mergeu_u_tupledu_u_primitive]: !_12. (!y diff__merge__tupled cmp a b l m. happ (happ (happ (happ (happ (happ (happ _12 y) diff__merge__tupled) cmp) a) b) l) m = h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/list/CONS (h4/pair/_2C a b) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))))) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m))) (happ diff__merge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))))) ==> (!_11. (!diff__merge__tupled cmp a b l y. happ (happ (happ (happ (happ (happ _11 diff__merge__tupled) cmp) a) b) l) y = happ (happ (happ (happ (happ (happ _12 y) diff__merge__tupled) cmp) a) b) l) ==> (!_10. (!v3 diff__merge__tupled cmp a l b. happ (happ (happ (happ (happ (happ _10 v3) diff__merge__tupled) cmp) a) l) b = h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS (h4/pair/_2C a b) l)) (happ (happ (happ (happ (happ _11 diff__merge__tupled) cmp) a) b) l)) ==> (!_9. (!v3 diff__merge__tupled cmp l a. happ (happ (happ (happ (happ _9 v3) diff__merge__tupled) cmp) l) a = happ (happ (happ (happ (happ _10 v3) diff__merge__tupled) cmp) a) l) ==> (!_8. (!v4 v3 diff__merge__tupled cmp l. happ (happ (happ (happ (happ _8 v4) v3) diff__merge__tupled) cmp) l = h4/pair/pair__CASE v4 (happ (happ (happ (happ _9 v3) diff__merge__tupled) cmp) l)) ==> (!_7. (!v3 diff__merge__tupled cmp v4. happ (happ (happ (happ _7 v3) diff__merge__tupled) cmp) v4 = happ (happ (happ (happ _8 v4) v3) diff__merge__tupled) cmp) ==> (!_6. (!v2 diff__merge__tupled cmp v3. happ (happ (happ (happ _6 v2) diff__merge__tupled) cmp) v3 = h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (happ (happ (happ _7 v3) diff__merge__tupled) cmp)) ==> (!_5. (!diff__merge__tupled cmp v2. happ (happ (happ _5 diff__merge__tupled) cmp) v2 = happ (happ (happ _6 v2) diff__merge__tupled) cmp) ==> (!_4. (!diff__merge__tupled cmp v1. happ (happ (happ _4 diff__merge__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 diff__merge__tupled) cmp)) ==> (!_3. (!diff__merge__tupled cmp. happ (happ _3 diff__merge__tupled) cmp = happ (happ _4 diff__merge__tupled) cmp) ==> (!_2. (!diff__merge__tupled a_27. happ (happ _2 diff__merge__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 diff__merge__tupled)) ==> (!_1. (!diff__merge__tupled. happ _1 diff__merge__tupled = happ _2 diff__merge__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!m l b y a cmp. h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m)))) /\ (!b m l y a cmp. h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m))))) ==> h4/fmapal/diff__merge__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_fmapals_interu_u_merge0u_c3]: !y m l cmp b a. h4/fmapal/inter__merge cmp (h4/list/CONS (h4/pair/_2C a b) l) (h4/list/CONS y m) = h4/toto/cpn__CASE (h4/toto/apto cmp a y) (h4/fmapal/inter__merge cmp l (h4/list/CONS y m)) (h4/list/CONS (h4/pair/_2C a b) (h4/fmapal/inter__merge cmp l m)) (h4/fmapal/inter__merge cmp (h4/list/CONS (h4/pair/_2C a b) l) m)
% Assm [h4s_fmapals_ORLu_u_tupledu_u_primitive]: !_8. (!ORL__tupled l cmp a b. ?v. (v <=> happ ORL__tupled (h4/pair/_2C cmp l) /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)) /\ (happ (happ (happ (happ (happ _8 ORL__tupled) l) cmp) a) b <=> h4/combin/I v)) ==> (!_7. (!ORL__tupled l cmp a. happ (happ (happ (happ _7 ORL__tupled) l) cmp) a = happ (happ (happ (happ _8 ORL__tupled) l) cmp) a) ==> (!_6. (!v2 ORL__tupled cmp l. happ (happ (happ (happ _6 v2) ORL__tupled) cmp) l <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 ORL__tupled) l) cmp)) ==> (!_5. (!ORL__tupled cmp v2. happ (happ (happ _5 ORL__tupled) cmp) v2 = happ (happ (happ _6 v2) ORL__tupled) cmp) ==> (!_4. (!ORL__tupled cmp v1. happ (happ (happ _4 ORL__tupled) cmp) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 ORL__tupled) cmp)) ==> (!_3. (!ORL__tupled cmp. happ (happ _3 ORL__tupled) cmp = happ (happ _4 ORL__tupled) cmp) ==> (!_2. (!ORL__tupled a_27. happ (happ _2 ORL__tupled) a_27 <=> h4/pair/pair__CASE a_27 (happ _3 ORL__tupled)) ==> (!_1. (!ORL__tupled. happ _1 ORL__tupled = happ _2 ORL__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!b a l cmp. happ (happ R (h4/pair/_2C cmp l)) (h4/pair/_2C cmp (h4/list/CONS (h4/pair/_2C a b) l)))) ==> h4/fmapal/ORL__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% 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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_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_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% 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_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% 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_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_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_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_fmapals_ORL0u_c1]: !l cmp b a. h4/fmapal/ORL cmp (h4/list/CONS (h4/pair/_2C a b) l) <=> h4/fmapal/ORL cmp l /\ (!p q. h4/bool/IN (h4/pair/_2C p q) (h4/list/LIST__TO__SET l) ==> h4/toto/apto cmp a p = h4/toto/LESS)
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> 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_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_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_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_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% 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_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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> 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_ltu_c1]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ]: !p n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/_2B m p)) (h4/arithmetic/_2B n p) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_LEFTu_u_ORu_u_EXISTSu_u_THM]: !Q P. (?x. happ P x) \/ Q <=> (?x. happ P x \/ Q)
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_fmapals_assocvu_u_tupledu_u_primitive]: !_8. (!x assocv__tupled l a y. ?v. (v <=> a = x) /\ happ (happ (happ (happ (happ _8 x) assocv__tupled) l) a) y = h4/combin/I (h4/bool/COND v (h4/option/SOME y) (happ assocv__tupled (h4/pair/_2C l a)))) ==> (!_7. (!assocv__tupled l a x. happ (happ (happ (happ _7 assocv__tupled) l) a) x = happ (happ (happ (happ _8 x) assocv__tupled) l) a) ==> (!_6. (!v2 assocv__tupled a l. happ (happ (happ (happ _6 v2) assocv__tupled) a) l = h4/pair/pair__CASE v2 (happ (happ (happ _7 assocv__tupled) l) a)) ==> (!_5. (!assocv__tupled a v2. happ (happ (happ _5 assocv__tupled) a) v2 = happ (happ (happ _6 v2) assocv__tupled) a) ==> (!_4. (!v assocv__tupled a. happ (happ (happ _4 v) assocv__tupled) a = h4/list/list__CASE v (h4/combin/I h4/option/NONE) (happ (happ _5 assocv__tupled) a)) ==> (!_3. (!assocv__tupled v. happ (happ _3 assocv__tupled) v = happ (happ _4 v) assocv__tupled) ==> (!_2. (!assocv__tupled a_27. happ (happ _2 assocv__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 assocv__tupled)) ==> (!_1. (!assocv__tupled. happ _1 assocv__tupled = happ _2 assocv__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y l x a. ~(a = x) ==> happ (happ R (h4/pair/_2C l a)) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C x y) l) a))) ==> h4/fmapal/assocv__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_fmapals_assocvu_u_ind]: !P. (!a. happ (happ P h4/list/NIL) a) /\ (!x y l a. (~(a = x) ==> happ (happ P l) a) ==> happ (happ P (h4/list/CONS (h4/pair/_2C x y) l)) a) ==> (!v v1. happ (happ P v) v1)
% Assm [h4s_fmapals_assocv0u_c1]: !y x l a. ?v. (v <=> a = x) /\ h4/fmapal/assocv (h4/list/CONS (h4/pair/_2C x y) l) a = h4/bool/COND v (h4/option/SOME y) (h4/fmapal/assocv l a)
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_tupledu_u_primitive]: !_11. (!x r bt__to__orl__ub__tupled cmp l ub y. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ happ (happ (happ (happ (happ (happ (happ _11 x) r) bt__to__orl__ub__tupled) cmp) l) ub) y = h4/combin/I (h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (happ bt__to__orl__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C l x))) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (happ bt__to__orl__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C l ub))))) ==> (!_10. (!r bt__to__orl__ub__tupled cmp l ub x. happ (happ (happ (happ (happ (happ _10 r) bt__to__orl__ub__tupled) cmp) l) ub) x = happ (happ (happ (happ (happ (happ _11 x) r) bt__to__orl__ub__tupled) cmp) l) ub) ==> (!_9. (!v5 bt__to__orl__ub__tupled cmp l ub r. happ (happ (happ (happ (happ (happ _9 v5) bt__to__orl__ub__tupled) cmp) l) ub) r = h4/pair/pair__CASE v5 (happ (happ (happ (happ (happ _10 r) bt__to__orl__ub__tupled) cmp) l) ub)) ==> (!_8. (!bt__to__orl__ub__tupled cmp l ub v5. happ (happ (happ (happ (happ _8 bt__to__orl__ub__tupled) cmp) l) ub) v5 = happ (happ (happ (happ (happ _9 v5) bt__to__orl__ub__tupled) cmp) l) ub) ==> (!_7. (!bt__to__orl__ub__tupled cmp ub l. happ (happ (happ (happ _7 bt__to__orl__ub__tupled) cmp) ub) l = happ (happ (happ (happ _8 bt__to__orl__ub__tupled) cmp) l) ub) ==> (!_6. (!v2 bt__to__orl__ub__tupled cmp ub. happ (happ (happ (happ _6 v2) bt__to__orl__ub__tupled) cmp) ub = h4/enumeral/bt__CASE v2 (h4/combin/I h4/list/NIL) (happ (happ (happ _7 bt__to__orl__ub__tupled) cmp) ub)) ==> (!_5. (!bt__to__orl__ub__tupled cmp v2. happ (happ (happ _5 bt__to__orl__ub__tupled) cmp) v2 = happ (happ (happ _6 v2) bt__to__orl__ub__tupled) cmp) ==> (!_4. (!bt__to__orl__ub__tupled cmp v1. happ (happ (happ _4 bt__to__orl__ub__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 bt__to__orl__ub__tupled) cmp)) ==> (!_3. (!bt__to__orl__ub__tupled cmp. happ (happ _3 bt__to__orl__ub__tupled) cmp = happ (happ _4 bt__to__orl__ub__tupled) cmp) ==> (!_2. (!bt__to__orl__ub__tupled a. happ (happ _2 bt__to__orl__ub__tupled) a = h4/pair/pair__CASE a (happ _3 bt__to__orl__ub__tupled)) ==> (!_1. (!bt__to__orl__ub__tupled. happ _1 bt__to__orl__ub__tupled = happ _2 bt__to__orl__ub__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!r y l ub x cmp. ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l ub))) (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub))) /\ (!r y l ub x cmp. h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l x))) (h4/pair/_2C cmp (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) ==> h4/fmapal/bt__to__orl__ub__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupledu_u_primitive]: !_13. (!x l bt__to__orl__lb__ub__tupled cmp lb r ub y. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ (?v'. (v' <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ happ (happ (happ (happ (happ (happ (happ (happ _13 x) l) bt__to__orl__lb__ub__tupled) cmp) lb) r) ub) y = h4/combin/I (h4/bool/COND v' (h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (happ bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l x)))) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (happ bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C x (h4/pair/_2C r ub))))) (happ bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l ub))))) (happ bt__to__orl__lb__ub__tupled (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C r ub))))))) ==> (!_12. (!l bt__to__orl__lb__ub__tupled cmp lb r ub x. happ (happ (happ (happ (happ (happ (happ _12 l) bt__to__orl__lb__ub__tupled) cmp) lb) r) ub) x = happ (happ (happ (happ (happ (happ (happ _13 x) l) bt__to__orl__lb__ub__tupled) cmp) lb) r) ub) ==> (!_11. (!v7 l bt__to__orl__lb__ub__tupled cmp lb ub r. happ (happ (happ (happ (happ (happ (happ _11 v7) l) bt__to__orl__lb__ub__tupled) cmp) lb) ub) r = h4/pair/pair__CASE v7 (happ (happ (happ (happ (happ (happ _12 l) bt__to__orl__lb__ub__tupled) cmp) lb) r) ub)) ==> (!_10. (!l bt__to__orl__lb__ub__tupled cmp lb ub v7. happ (happ (happ (happ (happ (happ _10 l) bt__to__orl__lb__ub__tupled) cmp) lb) ub) v7 = happ (happ (happ (happ (happ (happ _11 v7) l) bt__to__orl__lb__ub__tupled) cmp) lb) ub) ==> (!_9. (!bt__to__orl__lb__ub__tupled cmp lb ub l. happ (happ (happ (happ (happ _9 bt__to__orl__lb__ub__tupled) cmp) lb) ub) l = happ (happ (happ (happ (happ _10 l) bt__to__orl__lb__ub__tupled) cmp) lb) ub) ==> (!_8. (!v4 bt__to__orl__lb__ub__tupled cmp lb ub. happ (happ (happ (happ (happ _8 v4) bt__to__orl__lb__ub__tupled) cmp) lb) ub = h4/enumeral/bt__CASE v4 (h4/combin/I h4/list/NIL) (happ (happ (happ (happ _9 bt__to__orl__lb__ub__tupled) cmp) lb) ub)) ==> (!_7. (!bt__to__orl__lb__ub__tupled cmp lb v4. happ (happ (happ (happ _7 bt__to__orl__lb__ub__tupled) cmp) lb) v4 = happ (happ (happ (happ _8 v4) bt__to__orl__lb__ub__tupled) cmp) lb) ==> (!_6. (!bt__to__orl__lb__ub__tupled cmp lb v3. happ (happ (happ (happ _6 bt__to__orl__lb__ub__tupled) cmp) lb) v3 = h4/pair/pair__CASE v3 (happ (happ (happ _7 bt__to__orl__lb__ub__tupled) cmp) lb)) ==> (!_5. (!bt__to__orl__lb__ub__tupled cmp lb. happ (happ (happ _5 bt__to__orl__lb__ub__tupled) cmp) lb = happ (happ (happ _6 bt__to__orl__lb__ub__tupled) cmp) lb) ==> (!_4. (!bt__to__orl__lb__ub__tupled cmp v1. happ (happ (happ _4 bt__to__orl__lb__ub__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 bt__to__orl__lb__ub__tupled) cmp)) ==> (!_3. (!bt__to__orl__lb__ub__tupled cmp. happ (happ _3 bt__to__orl__lb__ub__tupled) cmp = happ (happ _4 bt__to__orl__lb__ub__tupled) cmp) ==> (!_2. (!bt__to__orl__lb__ub__tupled a. happ (happ _2 bt__to__orl__lb__ub__tupled) a = h4/pair/pair__CASE a (happ _3 bt__to__orl__lb__ub__tupled)) ==> (!_1. (!bt__to__orl__lb__ub__tupled. happ _1 bt__to__orl__lb__ub__tupled = happ _2 bt__to__orl__lb__ub__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y l ub r x lb cmp. ~(h4/toto/apto cmp lb x = h4/toto/LESS) ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C r ub)))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!r y l ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l ub)))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!r y l ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C l x)))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub)))) /\ (!y l r ub x lb cmp. h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C x (h4/pair/_2C r ub)))) (h4/pair/_2C cmp (h4/pair/_2C lb (h4/pair/_2C (h4/enumeral/node l (h4/pair/_2C x y) r) ub))))) ==> h4/fmapal/bt__to__orl__lb__ub__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))))
% Assm [h4s_fmapals_btu_u_tou_u_fmapu_u_tupledu_u_primitive]: !_11. (!cmp x z. ?v. (v <=> h4/toto/apto cmp x z = h4/toto/LESS) /\ happ (happ (happ _11 cmp) x) z = h4/pair/_2C z v) ==> (!_10. (!cmp x y. ?v. (v <=> h4/toto/apto cmp y x = h4/toto/LESS) /\ happ (happ (happ _10 cmp) x) y = h4/pair/_2C y v) ==> (!_9. (!l bt__to__fmap__tupled r cmp x v. happ (happ (happ (happ (happ (happ _9 l) bt__to__fmap__tupled) r) cmp) x) v = h4/combin/I (h4/finite__map/FUNION (h4/finite__map/FUNION (h4/finite__map/DRESTRICT (happ bt__to__fmap__tupled (h4/pair/_2C cmp l)) (h4/pred__set/GSPEC (happ (happ _10 cmp) x))) (h4/finite__map/FUPDATE h4/finite__map/FEMPTY (h4/pair/_2C x v))) (h4/finite__map/DRESTRICT (happ bt__to__fmap__tupled (h4/pair/_2C cmp r)) (h4/pred__set/GSPEC (happ (happ _11 cmp) x))))) ==> (!_8. (!l bt__to__fmap__tupled r cmp x. happ (happ (happ (happ (happ _8 l) bt__to__fmap__tupled) r) cmp) x = happ (happ (happ (happ (happ _9 l) bt__to__fmap__tupled) r) cmp) x) ==> (!_7. (!v4 l bt__to__fmap__tupled cmp r. happ (happ (happ (happ (happ _7 v4) l) bt__to__fmap__tupled) cmp) r = h4/pair/pair__CASE v4 (happ (happ (happ (happ _8 l) bt__to__fmap__tupled) r) cmp)) ==> (!_6. (!l bt__to__fmap__tupled cmp v4. happ (happ (happ (happ _6 l) bt__to__fmap__tupled) cmp) v4 = happ (happ (happ (happ _7 v4) l) bt__to__fmap__tupled) cmp) ==> (!_5. (!bt__to__fmap__tupled cmp l. happ (happ (happ _5 bt__to__fmap__tupled) cmp) l = happ (happ (happ _6 l) bt__to__fmap__tupled) cmp) ==> (!_4. (!bt__to__fmap__tupled cmp v2. happ (happ (happ _4 bt__to__fmap__tupled) cmp) v2 = h4/enumeral/bt__CASE v2 (h4/combin/I h4/finite__map/FEMPTY) (happ (happ _5 bt__to__fmap__tupled) cmp)) ==> (!_3. (!bt__to__fmap__tupled cmp. happ (happ _3 bt__to__fmap__tupled) cmp = happ (happ _4 bt__to__fmap__tupled) cmp) ==> (!_2. (!bt__to__fmap__tupled a. happ (happ _2 bt__to__fmap__tupled) a = h4/pair/pair__CASE a (happ _3 bt__to__fmap__tupled)) ==> (!_1. (!bt__to__fmap__tupled. happ _1 bt__to__fmap__tupled = happ _2 bt__to__fmap__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!r v x l cmp. happ (happ R (h4/pair/_2C cmp l)) (h4/pair/_2C cmp (h4/enumeral/node l (h4/pair/_2C x v) r))) /\ (!v x l r cmp. happ (happ R (h4/pair/_2C cmp r)) (h4/pair/_2C cmp (h4/enumeral/node l (h4/pair/_2C x v) r)))) ==> h4/fmapal/bt__to__fmap__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_ub0u_c1]: !y x ub r l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ h4/fmapal/bt__to__orl__ub cmp (h4/enumeral/node l (h4/pair/_2C x y) r) ub = h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (h4/fmapal/bt__to__orl__ub cmp l x) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (h4/fmapal/bt__to__orl__ub cmp l ub)
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub0u_c1]: !y x ub r lb l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ (?v'. (v' <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ h4/fmapal/bt__to__orl__lb__ub cmp lb (h4/enumeral/node l (h4/pair/_2C x y) r) ub = h4/bool/COND v' (h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (h4/fmapal/bt__to__orl__lb__ub cmp lb l x) (h4/list/CONS (h4/pair/_2C x y) h4/list/NIL)) (h4/fmapal/bt__to__orl__lb__ub cmp x r ub)) (h4/fmapal/bt__to__orl__lb__ub cmp lb l ub)) (h4/fmapal/bt__to__orl__lb__ub cmp lb r ub))
% Assm [h4s_fmapals_btu_u_tou_u_fmapu_c1]: !_1. (!cmp x z. ?v. (v <=> h4/toto/apto cmp x z = h4/toto/LESS) /\ happ (happ (happ _1 cmp) x) z = h4/pair/_2C z v) ==> (!_0. (!cmp x y. ?v. (v <=> h4/toto/apto cmp y x = h4/toto/LESS) /\ happ (happ (happ _0 cmp) x) y = h4/pair/_2C y v) ==> (!x v r l cmp. h4/fmapal/FMAPAL cmp (h4/enumeral/node l (h4/pair/_2C x v) r) = h4/finite__map/FUNION (h4/finite__map/FUNION (h4/finite__map/DRESTRICT (h4/fmapal/FMAPAL cmp l) (h4/pred__set/GSPEC (happ (happ _0 cmp) x))) (h4/finite__map/FUPDATE h4/finite__map/FEMPTY (h4/pair/_2C x v))) (h4/finite__map/DRESTRICT (h4/fmapal/FMAPAL cmp r) (h4/pred__set/GSPEC (happ (happ _1 cmp) x)))))
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_ind]: !P. (!cmp ub. happ (happ (happ P cmp) h4/enumeral/nt) ub) /\ (!cmp l x y r ub. (~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> happ (happ (happ P cmp) l) ub) /\ (h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ (happ P cmp) l) x) ==> happ (happ (happ P cmp) (h4/enumeral/node l (h4/pair/_2C x y) r)) ub) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_ind]: !P. (!cmp lb ub. happ (happ (happ (happ P cmp) lb) h4/enumeral/nt) ub) /\ (!cmp lb l x y r ub. (~(h4/toto/apto cmp lb x = h4/toto/LESS) ==> happ (happ (happ (happ P cmp) lb) r) ub) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ ~(h4/toto/apto cmp x ub = h4/toto/LESS) ==> happ (happ (happ (happ P cmp) lb) l) ub) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ (happ (happ P cmp) lb) l) x) /\ (h4/toto/apto cmp lb x = h4/toto/LESS /\ h4/toto/apto cmp x ub = h4/toto/LESS ==> happ (happ (happ (happ P cmp) x) r) ub) ==> happ (happ (happ (happ P cmp) lb) (h4/enumeral/node l (h4/pair/_2C x y) r)) ub) ==> (!v v1 v2 v3. happ (happ (happ (happ P v) v1) v2) v3)
% Assm [h4s_totos_aplextoto]: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_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_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_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_enumerals_btu_u_sizeu_u_defu_c1]: !f a2 a1 a0. h4/enumeral/bt__size f (h4/enumeral/node a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (happ f a1) (h4/enumeral/bt__size f a2)))
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c1]: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = happ (happ (happ f a0) a1) a2
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_fmapals_ORLu_u_curried]: !x1 x. h4/fmapal/ORL x x1 <=> happ h4/fmapal/ORL__tupled (h4/pair/_2C x x1)
% Assm [h4s_fmapals_interu_u_mergeu_u_curried]: !x2 x1 x. h4/fmapal/inter__merge x x1 x2 = happ h4/fmapal/inter__merge__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_totos_cpnu_u_caseu_u_cong]: !v2_27 v2 v1_27 v1 v0_27 v0 M_27 M. M = M_27 /\ (M_27 = h4/toto/LESS ==> v0 = v0_27) /\ (M_27 = h4/toto/EQUAL ==> v1 = v1_27) /\ (M_27 = h4/toto/GREATER ==> v2 = v2_27) ==> h4/toto/cpn__CASE M v0 v1 v2 = h4/toto/cpn__CASE M_27 v0_27 v1_27 v2_27
% Assm [h4s_enumerals_btu_u_nchotomy]: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = h4/enumeral/node b a b0)
% Assm [h4s_fmapals_assocvu_u_curried]: !x1 x. h4/fmapal/assocv x x1 = happ h4/fmapal/assocv__tupled (h4/pair/_2C x x1)
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_curried]: !x2 x1 x. h4/fmapal/bt__to__orl__ub x x1 x2 = happ h4/fmapal/bt__to__orl__ub__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_curried]: !x3 x2 x1 x. h4/fmapal/bt__to__orl__lb__ub x x1 x2 x3 = happ h4/fmapal/bt__to__orl__lb__ub__tupled (h4/pair/_2C x (h4/pair/_2C x1 (h4/pair/_2C x2 x3)))
% Assm [h4s_fmapals_btu_u_tou_u_fmapu_u_curried]: !x1 x. h4/fmapal/FMAPAL x x1 = happ h4/fmapal/bt__to__fmap__tupled (h4/pair/_2C x x1)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT2 m) <=> ~happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. happ (happ h4/prim__rec/_3C n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c20]: !n. happ (happ h4/prim__rec/_3C n) h4/num/0 <=> F
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_EQ]: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESS]: !p n m. happ (happ h4/prim__rec/_3C m) (h4/arithmetic/_2D n p) <=> happ (happ h4/prim__rec/_3C (h4/arithmetic/_2B m p)) n
% Goal: !P. (!cmp. happ (happ (happ P cmp) h4/list/NIL) h4/list/NIL) /\ (!cmp a b l. happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) h4/list/NIL) /\ (!cmp y m. happ (happ (happ P cmp) h4/list/NIL) (h4/list/CONS y m)) /\ (!cmp a b l y m. (h4/toto/apto cmp a y = h4/toto/EQUAL ==> happ (happ (happ P cmp) l) m) /\ (h4/toto/apto cmp a y = h4/toto/GREATER ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) m) /\ (h4/toto/apto cmp a y = h4/toto/LESS ==> happ (happ (happ P cmp) l) (h4/list/CONS y m)) ==> happ (happ (happ P cmp) (h4/list/CONS (h4/pair/_2C a b) l)) (h4/list/CONS y m)) ==> (!v v1 v2. happ (happ (happ P v) v1) v2)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1312288,TV_Q1312284]: ![V_f, V_g]: (![V_x]: s(TV_Q1312284,happ(s(t_fun(TV_Q1312288,TV_Q1312284),V_f),s(TV_Q1312288,V_x))) = s(TV_Q1312284,happ(s(t_fun(TV_Q1312288,TV_Q1312284),V_g),s(TV_Q1312288,V_x))) => s(t_fun(TV_Q1312288,TV_Q1312284),V_f) = s(t_fun(TV_Q1312288,TV_Q1312284),V_g))).
fof(ah4s_fmapals_interu_u_mergeu_u_ind, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_a, V_b, V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_y, V_m]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))) & ![V_cmp, V_a, V_b, V_l, V_y, V_m]: (((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_v))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))),s(t_h4s_lists_list(TV_u_27a),V_v2)))))).
fof(ah4s_fmapals_interu_u_mergeu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_12]: (![V_y, V_interu_u_mergeu_u_tupled, V_cmp, V_a, V_l, V_m, V_b]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))),s(TV_u_27b,V_b))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) => ![V_uu_11]: (![V_y, V_interu_u_mergeu_u_tupled, V_cmp, V_l, V_m, V_a]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))) => ![V_uu_10]: (![V_v4, V_y, V_interu_u_mergeu_u_tupled, V_cmp, V_l, V_m]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))) => ![V_uu_9]: (![V_v4, V_interu_u_mergeu_u_tupled, V_cmp, V_l, V_y]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_y))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) => ![V_uu_8]: (![V_v3, V_v4, V_interu_u_mergeu_u_tupled, V_cmp, V_l]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v3),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) => ![V_uu_7]: (![V_v3, V_interu_u_mergeu_u_tupled, V_cmp, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_6]: (![V_v2, V_interu_u_mergeu_u_tupled, V_cmp, V_v3]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_v3))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_interu_u_mergeu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_interu_u_mergeu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_interu_u_mergeu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_interu_u_mergeu_u_tupled, V_au_27]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))))) => ![V_uu_1]: (![V_interu_u_mergeu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_interu_u_mergeu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) & (![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & (![V_m, V_l, V_b, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & ![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_interu_u_mergeu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1))))))))))))))))).
fof(ah4s_fmapals_diffu_u_mergeu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_12]: (![V_y, V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_b, V_l, V_m]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) => ![V_uu_11]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_b, V_l, V_y]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_y))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_12),s(TV_u_27a,V_y))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) => ![V_uu_10]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_a, V_l, V_b]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27b,V_b))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v3),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) => ![V_uu_9]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_l, V_a]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) => ![V_uu_8]: (![V_v4, V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_l]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) => ![V_uu_7]: (![V_v3, V_diffu_u_mergeu_u_tupled, V_cmp, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_6]: (![V_v2, V_diffu_u_mergeu_u_tupled, V_cmp, V_v3]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_v3))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_diffu_u_mergeu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),V_v1),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_diffu_u_mergeu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_diffu_u_mergeu_u_tupled, V_au_27]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),V_au_27),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))))) => ![V_uu_1]: (![V_diffu_u_mergeu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_diffu_u_mergeu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) & (![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & (![V_m, V_l, V_b, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & ![V_b, V_m, V_l, V_y, V_a, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_diffu_u_mergeu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1))))))))))))))))).
fof(ah4s_fmapals_interu_u_merge0u_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_m, V_l, V_cmp, V_b, V_a]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_interu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_interu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_interu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_interu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m)))))).
fof(ah4s_fmapals_ORLu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_8]: (![V_ORLu_u_tupled, V_l, V_cmp, V_a, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) & ![V_p, V_q]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_p),s(TV_u_27b,V_q))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_p))) = s(t_h4s_totos_cpn,h4s_totos_less)))) & s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_ORLu_u_tupled, V_l, V_cmp, V_a]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_v2, V_ORLu_u_tupled, V_cmp, V_l]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_ORLu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_ORLu_u_tupled, V_cmp, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_ORLu_u_tupled, V_cmp]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_ORLu_u_tupled, V_au_27]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_au_27))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_au_27),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))))) => ![V_uu_1]: (![V_ORLu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),V_ORLu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) & ![V_b, V_a, V_l, V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_uu_1))))))))))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_bools_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_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_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_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_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_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_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_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_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_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_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_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_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_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_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_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_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_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_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_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_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_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_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_fmapals_ORL0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_cmp, V_b, V_a]: (p(s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) <=> (p(s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))) & ![V_p, V_q]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_p),s(TV_u_27b,V_q))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_p))) = s(t_h4s_totos_cpn,h4s_totos_less))))).
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_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_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_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_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_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_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_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_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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_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_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_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_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![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_bools_LEFTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))) <=> ?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_fmapals_assocvu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_8]: (![V_x, V_assocvu_u_tupled, V_l, V_a, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) & s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_8),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))),s(TV_u_27b,V_y))) = s(t_h4s_options_option(TV_u_27b),h4s_combins_i(s(t_h4s_options_option(TV_u_27b),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,V_y))),s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_a)))))))))) => ![V_uu_7]: (![V_assocvu_u_tupled, V_l, V_a, V_x]: s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_8),s(TV_u_27a,V_x))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_v2, V_assocvu_u_tupled, V_a, V_l]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_options_option(TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_options_option(TV_u_27b)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))))) => ![V_uu_5]: (![V_assocvu_u_tupled, V_a, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_6),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))) => ![V_uu_4]: (![V_v, V_assocvu_u_tupled, V_a]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))) = s(t_h4s_options_option(TV_u_27b),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v),s(t_h4s_options_option(TV_u_27b),h4s_combins_i(s(t_h4s_options_option(TV_u_27b),h4s_options_none))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_options_option(TV_u_27b))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(TV_u_27a,V_a))))) => ![V_uu_3]: (![V_assocvu_u_tupled, V_v]: s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))) = s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) => ![V_uu_2]: (![V_assocvu_u_tupled, V_au_27]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_au_27))) = s(t_h4s_options_option(TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_au_27),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))))) => ![V_uu_1]: (![V_assocvu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),V_assocvu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R)))) & ![V_y, V_l, V_x, V_a]: (~ (s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_a))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_fmapals_assocvu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b))),V_uu_1))))))))))))).
fof(ah4s_fmapals_assocvu_u_ind, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_a]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),V_P),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(TV_u_27a,V_a)))) & ![V_x, V_y, V_l, V_a]: ((~ (s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),V_P),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),V_P),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(TV_u_27a,V_a)))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),V_P),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v))),s(TV_u_27a,V_v1)))))).
fof(ah4s_fmapals_assocv0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_l, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_x)) & s(t_h4s_options_option(TV_u_27b),h4s_fmapals_assocv(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_a))) = s(t_h4s_options_option(TV_u_27b),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,V_y))),s(t_h4s_options_option(TV_u_27b),h4s_fmapals_assocv(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_a))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_11]: (![V_x, V_r, V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_l, V_ub, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))),s(TV_u_27b,V_y))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub)))))))))))) => ![V_uu_10]: (![V_r, V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_l, V_ub, V_x]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))) => ![V_uu_9]: (![V_v5, V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_l, V_ub, V_r]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))))) => ![V_uu_8]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_l, V_ub, V_v5]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_9),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v5))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))) => ![V_uu_7]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_ub, V_l]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_ub))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))) => ![V_uu_6]: (![V_v2, V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_ub]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_ub))))) => ![V_uu_5]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_v2]: s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_v1),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),V_a))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))))) => ![V_uu_1]: (![V_btu_u_tou_u_orlu_u_ubu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_ubu_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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool)),V_R)))) & (![V_r, V_y, V_l, V_ub, V_x, V_cmp]: (~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))))))) & ![V_r, V_y, V_l, V_ub, V_x, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1)))))))))))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_13]: (![V_x, V_l, V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_r, V_ub, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))))),V_uu_13),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))),s(TV_u_27b,V_y))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub))))))))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))))))))))))) => ![V_uu_12]: (![V_l, V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_r, V_ub, V_x]: s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))))),V_uu_12),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))))),V_uu_13),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))) => ![V_uu_11]: (![V_v7, V_l, V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_ub, V_r]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v7))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v7),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))))),V_uu_12),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))) => ![V_uu_10]: (![V_l, V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_ub, V_v7]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v7))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_11),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v7))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))) => ![V_uu_9]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_ub, V_l]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_10),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))) => ![V_uu_8]: (![V_v4, V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_ub]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v4),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(TV_u_27a,V_ub))))) => ![V_uu_7]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_v4]: s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v4))) = s(t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))) => ![V_uu_6]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb, V_v3]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_v3))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),V_v3),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))))) => ![V_uu_5]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_lb]: s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))) = s(t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))) => ![V_uu_4]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),V_v1))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),V_v1),s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),V_a))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))))) => ![V_uu_1]: (![V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_btu_u_tou_u_orlu_u_lbu_u_ubu_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(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R)))) & (![V_y, V_l, V_ub, V_r, V_x, V_lb, V_cmp]: (~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))))))))) & (![V_r, V_y, V_l, V_ub, V_x, V_lb, V_cmp]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & ~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))))))))) & (![V_r, V_y, V_l, V_ub, V_x, V_lb, V_cmp]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))))))))) & ![V_y, V_l, V_r, V_ub, V_x, V_lb, V_cmp]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_lb),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub)))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),V_uu_1)))))))))))))))))).
fof(ah4s_fmapals_btu_u_tou_u_fmapu_u_tupledu_u_primitive, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_11]: (![V_cmp, V_x, V_z]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_11),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(TV_u_27a,V_z))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_z),s(t_bool,V_v)))) => ![V_uu_10]: (![V_cmp, V_x, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_10),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_y),s(t_bool,V_v)))) => ![V_uu_9]: (![V_l, V_btu_u_tou_u_fmapu_u_tupled, V_r, V_cmp, V_x, V_v]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))))),V_uu_9),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(TV_u_27b,V_v))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_combins_i(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_10),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))))))),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),h4s_finiteu_u_maps_fempty),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_v))))))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_11),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))))))))))) => ![V_uu_8]: (![V_l, V_btu_u_tou_u_fmapu_u_tupled, V_r, V_cmp, V_x]: s(t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))))),V_uu_9),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))) => ![V_uu_7]: (![V_v4, V_l, V_btu_u_tou_u_fmapu_u_tupled, V_cmp, V_r]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_7),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))))),V_uu_8),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_6]: (![V_l, V_btu_u_tou_u_fmapu_u_tupled, V_cmp, V_v4]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_7),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v4))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_5]: (![V_btu_u_tou_u_fmapu_u_tupled, V_cmp, V_l]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_6),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_btu_u_tou_u_fmapu_u_tupled, V_cmp, V_v2]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_combins_i(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty))),s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_btu_u_tou_u_fmapu_u_tupled, V_cmp]: s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_btu_u_tou_u_fmapu_u_tupled, V_a]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_a))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))))) => ![V_uu_1]: (![V_btu_u_tou_u_fmapu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),V_btu_u_tou_u_fmapu_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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R)))) & (![V_r, V_v, V_x, 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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_v))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r)))))))) & ![V_v, V_x, V_l, V_r, V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_v))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_fmapu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),V_uu_1)))))))))))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_ub0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_ub, V_r, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_ub, V_r, V_lb, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r),s(TV_u_27a,V_ub)))))))).
fof(ah4s_fmapals_btu_u_tou_u_fmapu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_1]: (![V_cmp, V_x, V_z]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_1),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(TV_u_27a,V_z))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_z),s(t_bool,V_v)))) => ![V_uu_0]: (![V_cmp, V_x, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_y),s(t_bool,V_v)))) => ![V_x, V_v, V_r, V_l, V_cmp]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmapal(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_v))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmapal(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))))))),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),h4s_finiteu_u_maps_fempty),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_v))))))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmapal(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_1),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x)))))))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_ind, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_cmp, V_ub]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_nt))),s(TV_u_27a,V_ub)))) & ![V_cmp, V_l, V_x, V_y, V_r, V_ub]: (((~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))))) & (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_x)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))),s(TV_u_27a,V_ub)))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_v))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))),s(TV_u_27a,V_v2)))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_ind, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_cmp, V_lb, V_ub]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_nt))),s(TV_u_27a,V_ub)))) & ![V_cmp, V_lb, V_l, V_x, V_y, V_r, V_ub]: (((~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub))))) & (((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & ~ (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_ub))))) & (((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(TV_u_27a,V_x))))) & ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))),s(TV_u_27a,V_ub)))))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_lb))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_enumerals_node(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l),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_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_r))))),s(TV_u_27a,V_ub)))))) => ![V_v, V_v1, V_v2, V_v3]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_bool)))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_v))),s(TV_u_27a,V_v1))),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v2))),s(TV_u_27a,V_v3)))))).
fof(ah4s_totos_aplextoto, axiom, ![TV_u_27a,TV_u_27b]: ![V_y2, V_y1, V_x2, V_x1, V_v, V_c]: s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_lextoto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(t_h4s_totos_toto(TV_u_27b),V_v))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(TV_u_27b,V_x2))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_y1),s(TV_u_27b,V_y2))))) = s(t_h4s_totos_cpn,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x1),s(TV_u_27a,V_y1))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27b),V_v),s(TV_u_27b,V_x2),s(TV_u_27b,V_y2))),s(t_h4s_totos_cpn,h4s_totos_greater)))).
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_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_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_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_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_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_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_enumerals_btu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_node(s(t_h4s_enumerals_bt(TV_u_27a),V_a0),s(TV_u_27a,V_a1),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))) = 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,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),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_a1))),s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,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_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_node(s(t_h4s_enumerals_bt(TV_u_27a),V_a0),s(TV_u_27a,V_a1),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_fmapals_ORLu_u_curried, axiom, ![TV_u_27a,TV_u_27b]: ![V_x1, V_x]: s(t_bool,h4s_fmapals_orl(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_bool),h4s_fmapals_orlu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1)))))).
fof(ah4s_fmapals_interu_u_mergeu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_interu_u_merge(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x2))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_interu_u_mergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(t_h4s_lists_list(TV_u_27a),V_x2)))))))).
fof(ah4s_totos_cpnu_u_caseu_u_cong, axiom, ![TV_u_27a]: ![V_v2u_27, V_v2, V_v1u_27, V_v1, V_v0u_27, V_v0, V_Mu_27, V_M]: ((s(t_h4s_totos_cpn,V_M) = s(t_h4s_totos_cpn,V_Mu_27) & ((s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_less) => s(TV_u_27a,V_v0) = s(TV_u_27a,V_v0u_27)) & ((s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_equal) => s(TV_u_27a,V_v1) = s(TV_u_27a,V_v1u_27)) & (s(t_h4s_totos_cpn,V_Mu_27) = s(t_h4s_totos_cpn,h4s_totos_greater) => s(TV_u_27a,V_v2) = s(TV_u_27a,V_v2u_27))))) => s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,V_M),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,V_Mu_27),s(TV_u_27a,V_v0u_27),s(TV_u_27a,V_v1u_27),s(TV_u_27a,V_v2u_27))))).
fof(ah4s_enumerals_btu_u_nchotomy, axiom, ![TV_u_27a]: ![V_bb]: (s(t_h4s_enumerals_bt(TV_u_27a),V_bb) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) | ?[V_b, V_a, V_b0]: s(t_h4s_enumerals_bt(TV_u_27a),V_bb) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_node(s(t_h4s_enumerals_bt(TV_u_27a),V_b),s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))))).
fof(ah4s_fmapals_assocvu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x1, V_x]: s(t_h4s_options_option(TV_u_27b),h4s_fmapals_assocv(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x),s(TV_u_27a,V_x1))) = s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),t_h4s_options_option(TV_u_27b)),h4s_fmapals_assocvu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x),s(TV_u_27a,V_x1)))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(TV_u_27a,V_x2))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1),s(TV_u_27a,V_x2)))))))).
fof(ah4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_curried, axiom, ![TV_u_27b,TV_u_27a]: ![V_x3, V_x2, V_x1, V_x]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_x),s(TV_u_27a,V_x1),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x2),s(TV_u_27a,V_x3))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_fmapals_btu_u_tou_u_orlu_u_lbu_u_ubu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(t_h4s_pairs_prod(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27a),h4s_pairs_u_2c(s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x2),s(TV_u_27a,V_x3)))))))))).
fof(ah4s_fmapals_btu_u_tou_u_fmapu_u_curried, axiom, ![TV_u_27a,TV_u_27b]: ![V_x1, V_x]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_fmapals_fmapal(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b)),h4s_fmapals_btu_u_tou_u_fmapu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_x),s(t_h4s_enumerals_bt(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_x1)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_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,f)).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_numerals_numeralu_u_ltu_c5, 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,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,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))))))).
fof(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),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_ltu_c2, 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,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_ltu_c3, 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,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_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_n))),s(t_h4s_nums_num,V_m)))).
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_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c20, 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,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,f)).
fof(ah4s_numerals_iSUBu_u_THMu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),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_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (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_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
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_arithmetics_SUBu_u_LEFTu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) <=> (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,V_n) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0)))) & 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_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_LESS, axiom, ![V_p, V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))),s(t_h4s_nums_num,V_n)))).
fof(ch4s_fmapals_diffu_u_mergeu_u_ind, conjecture, ![TV_u_27b,TV_u_27a]: ![V_P]: ((![V_cmp]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_a, V_b, V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & (![V_cmp, V_y, V_m]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))) & ![V_cmp, V_a, V_b, V_l, V_y, V_m]: (((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),V_m))))) & (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_a),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m)))))))))) => ![V_v, V_v1, V_v2]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(t_h4s_lists_list(TV_u_27a),t_bool))),V_P),s(t_h4s_totos_toto(TV_u_27a),V_v))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_v1))),s(t_h4s_lists_list(TV_u_27a),V_v2)))))).
