%   ORIGINAL: h4/alist/alist__to__fmap__to__alist
% 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/FALSITY: !t. F ==> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/option/SOME__11: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/option/THE__DEF: !x. h4/option/THE (h4/option/SOME x) = x
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/pair__CASES: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/list/MAP__EQ__f: !l f2 f1. h4/list/MAP f1 l = h4/list/MAP f2 l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> f1 e = f2 e)
% Assm: h4/list/MEM__MAP: !x l f. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/MAP f l)) <=> (?y. x = f y /\ h4/bool/IN y (h4/list/LIST__TO__SET l))
% Assm: h4/list/FINITE__LIST__TO__SET: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% Assm: h4/list/MEM__SET__TO__LIST: !s. h4/pred__set/FINITE s ==> (!x. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/SET__TO__LIST s)) <=> h4/bool/IN x s)
% Assm: h4/alist/fmap__to__alist__def: !s. h4/alist/fmap__to__alist s = h4/list/MAP (\k. h4/pair/_2C k (h4/finite__map/FAPPLY s k)) (h4/list/SET__TO__LIST (h4/finite__map/FDOM s))
% Assm: h4/alist/ALOOKUP__FAILS: !x l. h4/alist/ALOOKUP l x = h4/option/NONE <=> (!k v. h4/bool/IN (h4/pair/_2C k v) (h4/list/LIST__TO__SET l) ==> ~(k = x))
% Assm: h4/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap: !v k al. h4/alist/ALOOKUP al k = h4/option/SOME v ==> h4/finite__map/FAPPLY (h4/alist/alist__to__fmap al) k = v
% Assm: h4/alist/FDOM__alist__to__fmap: !al. h4/finite__map/FDOM (h4/alist/alist__to__fmap al) = h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST al)
% Goal: !al. h4/alist/fmap__to__alist (h4/alist/alist__to__fmap al) = h4/list/MAP (\k. h4/pair/_2C k (h4/option/THE (h4/alist/ALOOKUP al k))) (h4/list/SET__TO__LIST (h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST al)))
%   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_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm [h4s_options_SOMEu_u_11]: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm [h4s_options_THEu_u_DEF]: !x. h4/option/THE (h4/option/SOME x) = x
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_pairs_pairu_u_CASES]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_pairs_FST0]: !y x. happ h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_lists_MAPu_u_EQu_u_f]: !l f2 f1. h4/list/MAP f1 l = h4/list/MAP f2 l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> happ f1 e = happ f2 e)
% Assm [h4s_lists_MEMu_u_MAP]: !x l f. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/MAP f l)) <=> (?y. x = happ f y /\ h4/bool/IN y (h4/list/LIST__TO__SET l))
% Assm [h4s_lists_FINITEu_u_LISTu_u_TOu_u_SET]: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% Assm [h4s_lists_MEMu_u_SETu_u_TOu_u_LIST]: !s. h4/pred__set/FINITE s ==> (!x. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/SET__TO__LIST s)) <=> h4/bool/IN x s)
% Assm [h4s_alists_fmapu_u_tou_u_alistu_u_def]: !_0. (!s k. happ (happ _0 s) k = h4/pair/_2C k (h4/finite__map/FAPPLY s k)) ==> (!s. h4/alist/fmap__to__alist s = h4/list/MAP (happ _0 s) (h4/list/SET__TO__LIST (h4/finite__map/FDOM s)))
% Assm [h4s_alists_ALOOKUPu_u_FAILS]: !x l. h4/alist/ALOOKUP l x = h4/option/NONE <=> (!k v. h4/bool/IN (h4/pair/_2C k v) (h4/list/LIST__TO__SET l) ==> ~(k = x))
% Assm [h4s_alists_ALOOKUPu_u_SOMEu_u_FAPPLYu_u_alistu_u_tou_u_fmap]: !v k al. h4/alist/ALOOKUP al k = h4/option/SOME v ==> h4/finite__map/FAPPLY (h4/alist/alist__to__fmap al) k = v
% Assm [h4s_alists_FDOMu_u_alistu_u_tou_u_fmap]: !al. h4/finite__map/FDOM (h4/alist/alist__to__fmap al) = h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST al)
% Goal: !_0. (!al k. happ (happ _0 al) k = h4/pair/_2C k (h4/option/THE (h4/alist/ALOOKUP al k))) ==> (!al. h4/alist/fmap__to__alist (h4/alist/alist__to__fmap al) = h4/list/MAP (happ _0 al) (h4/list/SET__TO__LIST (h4/list/LIST__TO__SET (h4/list/MAP h4/pair/FST al))))
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_Q270765,TV_Q270761]: ![V_f, V_g]: (![V_x]: s(TV_Q270761,happ(s(t_fun(TV_Q270765,TV_Q270761),V_f),s(TV_Q270765,V_x))) = s(TV_Q270761,happ(s(t_fun(TV_Q270765,TV_Q270761),V_g),s(TV_Q270765,V_x))) => s(t_fun(TV_Q270765,TV_Q270761),V_f) = s(t_fun(TV_Q270765,TV_Q270761),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
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_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_options_SOMEu_u_11, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_options_THEu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_options_the(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_pairu_u_CASES, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_MAPu_u_EQu_u_f, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f2, V_f1]: (s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f2),s(t_h4s_lists_list(TV_u_27a),V_l))) <=> ![V_e]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_e))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f2),s(TV_u_27a,V_e)))))).
fof(ah4s_lists_MEMu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27b,V_x),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l)))))))) <=> ?[V_y]: (s(TV_u_27b,V_x) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
fof(ah4s_lists_FINITEu_u_LISTu_u_TOu_u_SET, axiom, ![TV_u_27a]: ![V_l]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_lists_MEMu_u_SETu_u_TOu_u_LIST, axiom, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),V_s))))))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_alists_fmapu_u_tou_u_alistu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_s, V_k]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_0),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s))),s(TV_u_27a,V_k))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_k),s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s),s(TV_u_27a,V_k))))) => ![V_s]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_map(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_0),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s))))))))).
fof(ah4s_alists_ALOOKUPu_u_FAILS, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_l]: (s(t_h4s_options_option(TV_u_27a),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_l),s(TV_u_27b,V_x))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) <=> ![V_k, V_v]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27b,V_k),s(TV_u_27a,V_v))),s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_l)))))) => ~ (s(TV_u_27b,V_k) = s(TV_u_27b,V_x))))).
fof(ah4s_alists_ALOOKUPu_u_SOMEu_u_FAPPLYu_u_alistu_u_tou_u_fmap, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_k, V_al]: (s(t_h4s_options_option(TV_u_27b),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al),s(TV_u_27a,V_k))) = s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,V_v))) => s(TV_u_27b,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))),s(TV_u_27a,V_k))) = s(TV_u_27b,V_v))).
fof(ah4s_alists_FDOMu_u_alistu_u_tou_u_fmap, axiom, ![TV_u_27a,TV_u_27b]: ![V_al]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))))) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al)))))).
fof(ch4s_alists_alistu_u_tou_u_fmapu_u_tou_u_alist, conjecture, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_al, V_k]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_0),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))),s(TV_u_27a,V_k))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_k),s(TV_u_27b,h4s_options_the(s(t_h4s_options_option(TV_u_27b),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al),s(TV_u_27a,V_k))))))) => ![V_al]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_map(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),V_uu_0),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27a),h4s_pairs_fst),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_al))))))))))).
