%   ORIGINAL: h4/finite__map/SUBMAP__DRESTRICT
% 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/finite__map/DRESTRICT__SUBMAP: !r f. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f r) f
% Goal: !f P. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f P) f
%   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_finiteu_u_maps_DRESTRICTu_u_SUBMAP]: !r f. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f r) f
% Goal: !f P. h4/finite__map/SUBMAP (h4/finite__map/DRESTRICT f P) f
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_Q73550,TV_Q73546]: ![V_f, V_g]: (![V_x]: s(TV_Q73546,happ(s(t_fun(TV_Q73550,TV_Q73546),V_f),s(TV_Q73550,V_x))) = s(TV_Q73546,happ(s(t_fun(TV_Q73550,TV_Q73546),V_g),s(TV_Q73550,V_x))) => s(t_fun(TV_Q73550,TV_Q73546),V_f) = s(t_fun(TV_Q73550,TV_Q73546),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_finiteu_u_maps_DRESTRICTu_u_SUBMAP, axiom, ![TV_u_27a,TV_u_27b]: ![V_r, V_f]: 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_r))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))))).
fof(ch4s_finiteu_u_maps_SUBMAPu_u_DRESTRICT, conjecture, ![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))))).
