%   ORIGINAL: h4/finite__map/DRESTRICT__FUNION__SAME
% 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__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/finite__map/SUBMAP__DRESTRICT: !f P. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f P) f
% Assm: h4/finite__map/SUBMAP__FUNION__ABSORPTION: !g f. h4/finite__map/SUBMAP f g <=> h4/finite__map/FUNION f g = g
% Goal: !s fm. h4/finite__map/FUNION (h4/finite__map/DRESTRICT fm s) 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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_finiteu_u_maps_SUBMAPu_u_DRESTRICT]: !f P. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f P) f
% Assm [h4s_finiteu_u_maps_SUBMAPu_u_FUNIONu_u_ABSORPTION]: !g f. h4/finite__map/SUBMAP f g <=> h4/finite__map/FUNION f g = g
% Goal: !s fm. h4/finite__map/FUNION (h4/finite__map/DRESTRICT fm s) 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_Q77652,TV_Q77648]: ![V_f, V_g]: (![V_x]: s(TV_Q77648,happ(s(t_fun(TV_Q77652,TV_Q77648),V_f),s(TV_Q77652,V_x))) = s(TV_Q77648,happ(s(t_fun(TV_Q77652,TV_Q77648),V_g),s(TV_Q77652,V_x))) => s(t_fun(TV_Q77652,TV_Q77648),V_f) = s(t_fun(TV_Q77652,TV_Q77648),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_finiteu_u_maps_SUBMAPu_u_DRESTRICT, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_P]: p(s(t_bool,h4s_finiteu_u_maps_submap(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))))).
fof(ah4s_finiteu_u_maps_SUBMAPu_u_FUNIONu_u_ABSORPTION, axiom, ![TV_u_27a,TV_u_27b]: ![V_g, V_f]: (p(s(t_bool,h4s_finiteu_u_maps_submap(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_g)))) <=> s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(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_g))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g))).
fof(ch4s_finiteu_u_maps_DRESTRICTu_u_FUNIONu_u_SAME, conjecture, ![TV_u_27a,TV_u_27b]: ![V_s, V_fm]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(t_fun(TV_u_27a,t_bool),V_s))),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)).
