%   ORIGINAL: h4/alist/fmap__to__alist__to__fmap
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/finite__map/FLOOKUP__EXT: !f2 f1. f1 = f2 <=> h4/finite__map/FLOOKUP f1 = h4/finite__map/FLOOKUP f2
% Assm: h4/alist/ALOOKUP__EQ__FLOOKUP_c0: !al. h4/finite__map/FLOOKUP (h4/alist/alist__to__fmap al) = h4/alist/ALOOKUP al
% Assm: h4/alist/ALOOKUP__EQ__FLOOKUP_c1: !fm. h4/alist/ALOOKUP (h4/alist/fmap__to__alist fm) = h4/finite__map/FLOOKUP fm
% Goal: !fm. h4/alist/alist__to__fmap (h4/alist/fmap__to__alist fm) = fm
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_finiteu_u_maps_FLOOKUPu_u_EXT]: !f2 f1. f1 = f2 <=> h4/finite__map/FLOOKUP f1 = h4/finite__map/FLOOKUP f2
% Assm [h4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c0]: !al. h4/finite__map/FLOOKUP (h4/alist/alist__to__fmap al) = h4/alist/ALOOKUP al
% Assm [h4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c1]: !fm. h4/alist/ALOOKUP (h4/alist/fmap__to__alist fm) = h4/finite__map/FLOOKUP fm
% Goal: !fm. h4/alist/alist__to__fmap (h4/alist/fmap__to__alist fm) = fm
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_Q270361,TV_Q270357]: ![V_f, V_g]: (![V_x]: s(TV_Q270357,happ(s(t_fun(TV_Q270361,TV_Q270357),V_f),s(TV_Q270361,V_x))) = s(TV_Q270357,happ(s(t_fun(TV_Q270361,TV_Q270357),V_g),s(TV_Q270361,V_x))) => s(t_fun(TV_Q270361,TV_Q270357),V_f) = s(t_fun(TV_Q270361,TV_Q270357),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_finiteu_u_maps_FLOOKUPu_u_EXT, axiom, ![TV_u_27a,TV_u_27b]: ![V_f2, V_f1]: (s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f1) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f2) <=> s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f1))) = s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f2))))).
fof(ah4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_al]: s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),h4s_finiteu_u_maps_flookup(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_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)))).
fof(ah4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c1, axiom, ![TV_u_27c,TV_u_27d]: ![V_fm]: s(t_fun(TV_u_27c,t_h4s_options_option(TV_u_27d)),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27c,TV_u_27d)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27d),V_fm))))) = s(t_fun(TV_u_27c,t_h4s_options_option(TV_u_27d)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27d),V_fm)))).
fof(ch4s_alists_fmapu_u_tou_u_alistu_u_tou_u_fmap, conjecture, ![TV_u_27a,TV_u_27b]: ![V_fm]: 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)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm))))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm)).
