%   ORIGINAL: h4/finite__map/FDOM__FMERGE
% 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/FMERGE__DEF_c0: !m g f. h4/finite__map/FDOM (h4/finite__map/FMERGE m f g) = h4/pred__set/UNION (h4/finite__map/FDOM f) (h4/finite__map/FDOM g)
% Goal: !m g f. h4/finite__map/FDOM (h4/finite__map/FMERGE m f g) = h4/pred__set/UNION (h4/finite__map/FDOM f) (h4/finite__map/FDOM g)
%   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_FMERGEu_u_DEFu_c0]: !m g f. h4/finite__map/FDOM (h4/finite__map/FMERGE m f g) = h4/pred__set/UNION (h4/finite__map/FDOM f) (h4/finite__map/FDOM g)
% Goal: !m g f. h4/finite__map/FDOM (h4/finite__map/FMERGE m f g) = h4/pred__set/UNION (h4/finite__map/FDOM f) (h4/finite__map/FDOM g)
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_Q73856,TV_Q73852]: ![V_f, V_g]: (![V_x]: s(TV_Q73852,happ(s(t_fun(TV_Q73856,TV_Q73852),V_f),s(TV_Q73856,V_x))) = s(TV_Q73852,happ(s(t_fun(TV_Q73856,TV_Q73852),V_g),s(TV_Q73856,V_x))) => s(t_fun(TV_Q73856,TV_Q73852),V_f) = s(t_fun(TV_Q73856,TV_Q73852),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_FMERGEu_u_DEFu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_m, V_g, V_f]: s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_m),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_g))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_f))),s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_g)))))).
fof(ch4s_finiteu_u_maps_FDOMu_u_FMERGE, conjecture, ![TV_u_27b,TV_u_27a]: ![V_m, V_g, V_f]: s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),h4s_finiteu_u_maps_fmerge(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_m),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_g))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_f))),s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27a),V_g)))))).
