%   ORIGINAL: h4/fmapal/bt__to__fmap_c1
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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/enumeral/bt__case__def_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% 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/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__fmap__curried: !x1 x. h4/fmapal/FMAPAL x x1 = h4/fmapal/bt__to__fmap__tupled (h4/pair/_2C x x1)
% Goal: !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))))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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_enumerals_btu_u_caseu_u_defu_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% 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_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_fmapu_u_curried]: !x1 x. h4/fmapal/FMAPAL x x1 = happ h4/fmapal/bt__to__fmap__tupled (h4/pair/_2C x x1)
% Goal: !_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)))))
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_Q219158,TV_Q219154]: ![V_f, V_g]: (![V_x]: s(TV_Q219154,happ(s(t_fun(TV_Q219158,TV_Q219154),V_f),s(TV_Q219158,V_x))) = s(TV_Q219154,happ(s(t_fun(TV_Q219158,TV_Q219154),V_g),s(TV_Q219158,V_x))) => s(t_fun(TV_Q219158,TV_Q219154),V_f) = s(t_fun(TV_Q219158,TV_Q219154),V_g))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_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_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_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_pairs_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_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_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_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_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_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_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_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(ch4s_fmapals_btu_u_tou_u_fmapu_c1, conjecture, ![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)))))))))))).
