%   ORIGINAL: h4/HolSmt/r061
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/combin/APPLY__UPDATE__ID: !f a. h4/combin/UPDATE a (f a) f = f
% Goal: !x f. h4/combin/UPDATE x (f x) f = 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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_combins_APPLYu_u_UPDATEu_u_ID]: !f a. h4/combin/UPDATE a (happ f a) f = f
% Goal: !x f. h4/combin/UPDATE x (happ f x) f = 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_Q337282,TV_Q337278]: ![V_f, V_g]: (![V_x]: s(TV_Q337278,happ(s(t_fun(TV_Q337282,TV_Q337278),V_f),s(TV_Q337282,V_x))) = s(TV_Q337278,happ(s(t_fun(TV_Q337282,TV_Q337278),V_g),s(TV_Q337282,V_x))) => s(t_fun(TV_Q337282,TV_Q337278),V_f) = s(t_fun(TV_Q337282,TV_Q337278),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_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_combins_APPLYu_u_UPDATEu_u_ID, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_a]: s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_update(s(TV_u_27a,V_a),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27b),V_f)).
fof(ch4s_HolSmts_r061, conjecture, ![TV_u_27a,TV_u_27b]: ![V_x, V_f]: s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_update(s(TV_u_27a,V_x),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27b),V_f)).
