%   ORIGINAL: h4/finite__map/DRESTRICT__IDEMPOT
% 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/pred__set/INTER__IDEMPOT: !s. h4/pred__set/INTER s s = s
% Assm: h4/finite__map/DRESTRICT__DRESTRICT: !f Q P. h4/finite__map/DRESTRICT (h4/finite__map/DRESTRICT f P) Q = h4/finite__map/DRESTRICT f (h4/pred__set/INTER P Q)
% Goal: !vs s. h4/finite__map/DRESTRICT (h4/finite__map/DRESTRICT s vs) vs = h4/finite__map/DRESTRICT s vs
%   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_predu_u_sets_INTERu_u_IDEMPOT]: !s. h4/pred__set/INTER s s = s
% Assm [h4s_finiteu_u_maps_DRESTRICTu_u_DRESTRICT]: !f Q P. h4/finite__map/DRESTRICT (h4/finite__map/DRESTRICT f P) Q = h4/finite__map/DRESTRICT f (h4/pred__set/INTER P Q)
% Goal: !vs s. h4/finite__map/DRESTRICT (h4/finite__map/DRESTRICT s vs) vs = h4/finite__map/DRESTRICT s vs
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_Q76740,TV_Q76736]: ![V_f, V_g]: (![V_x]: s(TV_Q76736,happ(s(t_fun(TV_Q76740,TV_Q76736),V_f),s(TV_Q76740,V_x))) = s(TV_Q76736,happ(s(t_fun(TV_Q76740,TV_Q76736),V_g),s(TV_Q76740,V_x))) => s(t_fun(TV_Q76740,TV_Q76736),V_f) = s(t_fun(TV_Q76740,TV_Q76736),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_predu_u_sets_INTERu_u_IDEMPOT, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_finiteu_u_maps_DRESTRICTu_u_DRESTRICT, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_Q, V_P]: 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),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_fun(TV_u_27a,t_bool),V_Q))) = 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),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_Q)))))).
fof(ch4s_finiteu_u_maps_DRESTRICTu_u_IDEMPOT, conjecture, ![TV_u_27b,TV_u_27a]: ![V_vs, V_s]: 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),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_s),s(t_fun(TV_u_27a,t_bool),V_vs))),s(t_fun(TV_u_27a,t_bool),V_vs))) = 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_s),s(t_fun(TV_u_27a,t_bool),V_vs)))).
