%   ORIGINAL: h4/finite__map/FDOM__EQ__EMPTY__SYM
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/finite__map/FDOM__EQ__EMPTY: !f. h4/finite__map/FDOM f = h4/pred__set/EMPTY <=> f = h4/finite__map/FEMPTY
% Goal: !f. h4/pred__set/EMPTY = h4/finite__map/FDOM f <=> f = h4/finite__map/FEMPTY
%   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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_finiteu_u_maps_FDOMu_u_EQu_u_EMPTY]: !f. h4/finite__map/FDOM f = h4/pred__set/EMPTY <=> f = h4/finite__map/FEMPTY
% Goal: !f. h4/pred__set/EMPTY = h4/finite__map/FDOM f <=> f = h4/finite__map/FEMPTY
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q72768,TV_Q72764]: ![V_f, V_g]: (![V_x]: s(TV_Q72764,happ(s(t_fun(TV_Q72768,TV_Q72764),V_f),s(TV_Q72768,V_x))) = s(TV_Q72764,happ(s(t_fun(TV_Q72768,TV_Q72764),V_g),s(TV_Q72768,V_x))) => s(t_fun(TV_Q72768,TV_Q72764),V_f) = s(t_fun(TV_Q72768,TV_Q72764),V_g))).
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_finiteu_u_maps_FDOMu_u_EQu_u_EMPTY, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: (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_f))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty) <=> s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty))).
fof(ch4s_finiteu_u_maps_FDOMu_u_EQu_u_EMPTYu_u_SYM, conjecture, ![TV_u_27a,TV_u_27b]: ![V_f]: (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty) = 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_f))) <=> s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fempty))).
