%   ORIGINAL: h4/finite__map/FOLDL2__FUPDATE__LIST__paired
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY0: !v f. h4/pair/UNCURRY f v = f (h4/pair/FST v) (h4/pair/SND v)
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/LAMBDA__PROD: !P. (\p. P p) = h4/pair/UNCURRY (\p1 p2. P (h4/pair/_2C p1 p2))
% Assm: h4/list/LENGTH__MAP: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm: h4/list/LENGTH__ZIP: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l1 /\ h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l2
% Assm: h4/list/ZIP__MAP: !l2 l1 f2 f1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/ZIP (h4/pair/_2C (h4/list/MAP f1 l1) l2) = h4/list/MAP (\p. h4/pair/_2C (f1 (h4/pair/FST p)) (h4/pair/SND p)) (h4/list/ZIP (h4/pair/_2C l1 l2)) /\ h4/list/ZIP (h4/pair/_2C l1 (h4/list/MAP f2 l2)) = h4/list/MAP (\p. h4/pair/_2C (h4/pair/FST p) (f2 (h4/pair/SND p))) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm: h4/list/MAP2__MAP: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f. h4/list/MAP2 f l1 l2 = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C l1 l2)))
% Assm: h4/list/FOLDL2__FOLDL: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f a. h4/list/FOLDL2 f a l1 l2 = h4/list/FOLDL (\a0. h4/pair/UNCURRY (f a0)) a (h4/list/ZIP (h4/pair/_2C l1 l2)))
% Assm: h4/list/MAP__ZIP__SAME: !ls f. h4/list/MAP f (h4/list/ZIP (h4/pair/_2C ls ls)) = h4/list/MAP (\x. f (h4/pair/_2C x x)) ls
% Assm: h4/rich__list/FOLDL__MAP: !l g f e. h4/list/FOLDL f e (h4/list/MAP g l) = h4/list/FOLDL (\x y. f x (g y)) e l
% Assm: h4/finite__map/FUPDATE__LIST0: h4/finite__map/FUPDATE__LIST = h4/list/FOLDL h4/finite__map/FUPDATE
% Goal: !f2 f1 cs bs a. h4/list/LENGTH bs = h4/list/LENGTH cs ==> h4/list/FOLDL2 (\fm b. h4/pair/UNCURRY (\c d. h4/finite__map/FUPDATE fm (h4/pair/_2C (f1 b c d) (f2 b c d)))) a bs cs = h4/finite__map/FUPDATE__LIST a (h4/list/ZIP (h4/pair/_2C (h4/list/MAP2 (\b. h4/pair/UNCURRY (f1 b)) bs cs) (h4/list/MAP2 (\b. h4/pair/UNCURRY (f2 b)) bs cs)))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRY0]: !v f. happ (h4/pair/UNCURRY f) v = happ (happ f (h4/pair/FST v)) (h4/pair/SND v)
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_LAMBDAu_u_PROD]: !_1. (!P p1 p2. happ (happ (happ _1 P) p1) p2 = happ P (h4/pair/_2C p1 p2)) ==> (!_0. (!P p1. happ (happ _0 P) p1 = happ (happ _1 P) p1) ==> (!P x. happ P x = happ (h4/pair/UNCURRY (happ _0 P)) x))
% Assm [h4s_lists_LENGTHu_u_MAP]: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm [h4s_lists_LENGTHu_u_ZIP]: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l1 /\ h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l2
% Assm [h4s_lists_ZIPu_u_MAP]: !_1. (!f2 p. happ (happ _1 f2) p = h4/pair/_2C (h4/pair/FST p) (happ f2 (h4/pair/SND p))) ==> (!_0. (!f1 p. happ (happ _0 f1) p = h4/pair/_2C (happ f1 (h4/pair/FST p)) (h4/pair/SND p)) ==> (!l2 l1 f2 f1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/ZIP (h4/pair/_2C (h4/list/MAP f1 l1) l2) = h4/list/MAP (happ _0 f1) (h4/list/ZIP (h4/pair/_2C l1 l2)) /\ h4/list/ZIP (h4/pair/_2C l1 (h4/list/MAP f2 l2)) = h4/list/MAP (happ _1 f2) (h4/list/ZIP (h4/pair/_2C l1 l2))))
% Assm [h4s_lists_MAP2u_u_MAP]: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f. h4/list/MAP2 f l1 l2 = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C l1 l2)))
% Assm [h4s_lists_FOLDL2u_u_FOLDL]: !_0. (!f a0. happ (happ _0 f) a0 = h4/pair/UNCURRY (happ f a0)) ==> (!l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f a. h4/list/FOLDL2 f a l1 l2 = happ (happ (h4/list/FOLDL (happ _0 f)) a) (h4/list/ZIP (h4/pair/_2C l1 l2))))
% Assm [h4s_lists_MAPu_u_ZIPu_u_SAME]: !_0. (!f x. happ (happ _0 f) x = happ f (h4/pair/_2C x x)) ==> (!ls f. h4/list/MAP f (h4/list/ZIP (h4/pair/_2C ls ls)) = h4/list/MAP (happ _0 f) ls)
% Assm [h4s_richu_u_lists_FOLDLu_u_MAP]: !_1. (!f x g y. happ (happ (happ (happ _1 f) x) g) y = happ (happ f x) (happ g y)) ==> (!_0. (!f g x. happ (happ (happ _0 f) g) x = happ (happ (happ _1 f) x) g) ==> (!l g f e. happ (happ (h4/list/FOLDL f) e) (h4/list/MAP g l) = happ (happ (h4/list/FOLDL (happ (happ _0 f) g)) e) l))
% Assm [h4s_finiteu_u_maps_FUPDATEu_u_LIST0]: h4/finite__map/FUPDATE__LIST = h4/list/FOLDL h4/finite__map/FUPDATE
% Goal: !_5. (!f2 b. happ (happ _5 f2) b = h4/pair/UNCURRY (happ f2 b)) ==> (!_4. (!f1 b. happ (happ _4 f1) b = h4/pair/UNCURRY (happ f1 b)) ==> (!_3. (!fm f1 f2 b c d. happ (happ (happ (happ (happ (happ _3 fm) f1) f2) b) c) d = happ (happ h4/finite__map/FUPDATE fm) (h4/pair/_2C (happ (happ (happ f1 b) c) d) (happ (happ (happ f2 b) c) d))) ==> (!_2. (!fm f1 f2 b c. happ (happ (happ (happ (happ _2 fm) f1) f2) b) c = happ (happ (happ (happ (happ _3 fm) f1) f2) b) c) ==> (!_1. (!fm f1 f2 b. happ (happ (happ (happ _1 fm) f1) f2) b = h4/pair/UNCURRY (happ (happ (happ (happ _2 fm) f1) f2) b)) ==> (!_0. (!f1 f2 fm. happ (happ (happ _0 f1) f2) fm = happ (happ (happ _1 fm) f1) f2) ==> (!f2 f1 cs bs a. h4/list/LENGTH bs = h4/list/LENGTH cs ==> h4/list/FOLDL2 (happ (happ _0 f1) f2) a bs cs = happ (happ h4/finite__map/FUPDATE__LIST a) (h4/list/ZIP (h4/pair/_2C (h4/list/MAP2 (happ _4 f1) bs cs) (h4/list/MAP2 (happ _5 f2) bs cs)))))))))
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_Q77727,TV_Q77723]: ![V_f, V_g]: (![V_x]: s(TV_Q77723,happ(s(t_fun(TV_Q77727,TV_Q77723),V_f),s(TV_Q77727,V_x))) = s(TV_Q77723,happ(s(t_fun(TV_Q77727,TV_Q77723),V_g),s(TV_Q77727,V_x))) => s(t_fun(TV_Q77727,TV_Q77723),V_f) = s(t_fun(TV_Q77727,TV_Q77723),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_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_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_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_UNCURRY0, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))) = 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,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v)))))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_LAMBDAu_u_PROD, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_p1, V_p2]: 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)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_1),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P))),s(TV_u_27a,V_p1))),s(TV_u_27b,V_p2))) = s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_p1),s(TV_u_27b,V_p2))))) => ![V_uu_0]: (![V_P, V_p1]: s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P))),s(TV_u_27a,V_p1))) = s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_1),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P))),s(TV_u_27a,V_p1))) => ![V_P, V_x]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))) = s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),V_P))))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)))))).
fof(ah4s_lists_LENGTHu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_LENGTHu_u_ZIP, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) & s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2)))))).
fof(ah4s_lists_ZIPu_u_MAP, axiom, ![TV_u_27c,TV_u_27d,TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f2, V_p]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27d),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27a,TV_u_27d)),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27a,TV_u_27d))),V_uu_1),s(t_fun(TV_u_27b,TV_u_27d),V_f2))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27d),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))),s(TV_u_27d,happ(s(t_fun(TV_u_27b,TV_u_27d),V_f2),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))))))) => ![V_uu_0]: (![V_f1, V_p]: s(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_f1))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))) = s(t_h4s_pairs_prod(TV_u_27c,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_f1),s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))))) => ![V_l2, V_l1, V_f2, V_f1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => (s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27c),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27c),V_f1),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27b),V_l2))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_f1))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) & s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27d)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27d)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27d),h4s_lists_map(s(t_fun(TV_u_27b,TV_u_27d),V_f2),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27d)),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27a,TV_u_27d)),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27a,TV_u_27d))),V_uu_1),s(t_fun(TV_u_27b,TV_u_27d),V_f2))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))))))))))).
fof(ah4s_lists_MAP2u_u_MAP, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => ![V_f]: s(t_h4s_lists_list(TV_u_27c),h4s_lists_map2(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))) = s(t_h4s_lists_list(TV_u_27c),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))))).
fof(ah4s_lists_FOLDL2u_u_FOLDL, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_f, V_a0]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),t_fun(TV_u_27c,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c))),V_uu_0),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_f))),s(TV_u_27c,V_a0))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_f),s(TV_u_27c,V_a0))))) => ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => ![V_f, V_a]: s(TV_u_27c,h4s_lists_foldl2(s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_f),s(TV_u_27c,V_a),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))) = s(TV_u_27c,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27c),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),TV_u_27c)),h4s_lists_foldl(s(t_fun(TV_u_27c,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),t_fun(TV_u_27c,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c))),V_uu_0),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),V_f))))),s(TV_u_27c,V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))))))))).
fof(ah4s_lists_MAPu_u_ZIPu_u_SAME, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_x))))) => ![V_ls, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27a)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_ls),s(t_h4s_lists_list(TV_u_27a),V_ls))))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27a),V_ls))))).
fof(ah4s_richu_u_lists_FOLDLu_u_MAP, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_uu_1]: (![V_f, V_x, V_g, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_x))),s(t_fun(TV_u_27c,TV_u_27b),V_g))),s(TV_u_27c,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_g),s(TV_u_27c,V_y))))) => ![V_uu_0]: (![V_f, V_g, V_x]: s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(t_fun(TV_u_27c,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_x))),s(t_fun(TV_u_27c,TV_u_27b),V_g))) => ![V_l, V_g, V_f, V_e]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27c,TV_u_27b),V_g),s(t_h4s_lists_list(TV_u_27c),V_l))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(t_fun(TV_u_27c,TV_u_27b),V_g))))),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27c),V_l)))))).
fof(ah4s_finiteu_u_maps_FUPDATEu_u_LIST0, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdateu_u_list) = s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_lists_foldl(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b))),h4s_finiteu_u_maps_fupdate)))).
fof(ch4s_finiteu_u_maps_FOLDL2u_u_FUPDATEu_u_LISTu_u_paired, conjecture, ![TV_u_27d,TV_u_27e,TV_u_27a,TV_u_27b,TV_u_27c]: ![V_uu_5]: (![V_f2, V_b]: s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e))),V_uu_5),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))) = s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2),s(TV_u_27a,V_b))))) => ![V_uu_4]: (![V_f1, V_b]: s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d))),V_uu_4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(TV_u_27a,V_b))) = s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1),s(TV_u_27a,V_b))))) => ![V_uu_3]: (![V_fm, V_f1, V_f2, V_b, V_c, V_d]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),happ(s(t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))))),V_uu_3),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))),s(TV_u_27b,V_c))),s(TV_u_27c,V_d))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27d,TV_u_27e),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_h4s_pairs_prod(TV_u_27d,TV_u_27e),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),h4s_finiteu_u_maps_fupdate),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_h4s_pairs_prod(TV_u_27d,TV_u_27e),h4s_pairs_u_2c(s(TV_u_27d,happ(s(t_fun(TV_u_27c,TV_u_27d),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1),s(TV_u_27a,V_b))),s(TV_u_27b,V_c))),s(TV_u_27c,V_d))),s(TV_u_27e,happ(s(t_fun(TV_u_27c,TV_u_27e),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2),s(TV_u_27a,V_b))),s(TV_u_27b,V_c))),s(TV_u_27c,V_d))))))) => ![V_uu_2]: (![V_fm, V_f1, V_f2, V_b, V_c]: s(t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))))),V_uu_2),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))),s(TV_u_27b,V_c))) = s(t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))))),V_uu_3),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))),s(TV_u_27b,V_c))) => ![V_uu_1]: (![V_fm, V_f1, V_f2, V_b]: s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),V_uu_1),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))) = s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))))),V_uu_2),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(TV_u_27a,V_b))))) => ![V_uu_0]: (![V_f1, V_f2, V_fm]: s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))) = s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),V_uu_1),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_fm))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))) => ![V_f2, V_f1, V_cs, V_bs, V_a]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_bs))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27c)),V_cs))) => s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),h4s_lists_foldl2(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)))))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_a),s(t_h4s_lists_list(TV_u_27a),V_bs),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27c)),V_cs))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27d,TV_u_27e)),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27d,TV_u_27e)),t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e))),h4s_finiteu_u_maps_fupdateu_u_list),s(t_h4s_finiteu_u_maps_fmap(TV_u_27d,TV_u_27e),V_a))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27d,TV_u_27e)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27d),t_h4s_lists_list(TV_u_27e)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27d),h4s_lists_map2(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27d))),V_uu_4),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27d))),V_f1))),s(t_h4s_lists_list(TV_u_27a),V_bs),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27c)),V_cs))),s(t_h4s_lists_list(TV_u_27e),h4s_lists_map2(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),TV_u_27e))),V_uu_5),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27e))),V_f2))),s(t_h4s_lists_list(TV_u_27a),V_bs),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27c)),V_cs))))))))))))))))).
