%   ORIGINAL: h4/alist/fmap__to__alist__FEMPTY
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/SET__TO__LIST__EMPTY: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm: h4/finite__map/FDOM__FEMPTY: h4/finite__map/FDOM h4/finite__map/FEMPTY = h4/pred__set/EMPTY
% 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))
% Goal: h4/alist/fmap__to__alist h4/finite__map/FEMPTY = h4/list/NIL
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_SETu_u_TOu_u_LISTu_u_EMPTY]: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm [h4s_finiteu_u_maps_FDOMu_u_FEMPTY]: h4/finite__map/FDOM h4/finite__map/FEMPTY = h4/pred__set/EMPTY
% 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)))
% Goal: h4/alist/fmap__to__alist h4/finite__map/FEMPTY = h4/list/NIL
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_Q269979,TV_Q269975]: ![V_f, V_g]: (![V_x]: s(TV_Q269975,happ(s(t_fun(TV_Q269979,TV_Q269975),V_f),s(TV_Q269979,V_x))) = s(TV_Q269975,happ(s(t_fun(TV_Q269979,TV_Q269975),V_g),s(TV_Q269979,V_x))) => s(t_fun(TV_Q269979,TV_Q269975),V_f) = s(t_fun(TV_Q269979,TV_Q269975),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: 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),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_SETu_u_TOu_u_LISTu_u_EMPTY, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_finiteu_u_maps_FDOMu_u_FEMPTY, axiom, ![TV_u_27b,TV_u_27a]: 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_finiteu_u_maps_fempty))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
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(ch4s_alists_fmapu_u_tou_u_alistu_u_FEMPTY, conjecture, ![TV_u_27a,TV_u_27b]: 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_finiteu_u_maps_fempty))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil)).
