%   ORIGINAL: 'h4/thm/combin/UPDATE_APPLY_e1'
% 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
% Goal: !a b x f. ~(a = b) ==> 'h4/const/combin/UPDATE' a x f b = f b
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !a b x f. ~(a = b) ==> 'h4/const/combin/UPDATE' a x f b = happ f b
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f38655,V_3f38651]: ![F, G]: (![X]: s(V_3f38651,happ(s(fun(V_3f38655,V_3f38651),F),s(V_3f38655,X))) = s(V_3f38651,happ(s(fun(V_3f38655,V_3f38651),G),s(V_3f38655,X))) => s(fun(V_3f38655,V_3f38651),F) = s(fun(V_3f38655,V_3f38651),G))).
fof('h4/thm/combin/UPDATE_APPLY_e1', conjecture, ![D,C]: ![A, B, X, F]: (~ (s(C,A) = s(C,B)) => s(D,'h4/const/combin/UPDATE'(s(C,A),s(D,X),s(fun(C,D),F),s(C,B))) = s(D,happ(s(fun(C,D),F),s(C,B))))).
