%   ORIGINAL: 'h4/thm/combin/SAME_KEY_UPDATE_DIFFER_'
% 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: !f f1 f2 a b c. ~(b = c) ==> ~('h4/const/combin/UPDATE' a b f = 'h4/const/combin/UPDATE' a c f)
%   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: !f f1 f2 a b c. ~(b = c) ==> ~('h4/const/combin/UPDATE' a b f = 'h4/const/combin/UPDATE' a c f)
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_3f38856,V_3f38852]: ![F, G]: (![X]: s(V_3f38852,happ(s(fun(V_3f38856,V_3f38852),F),s(V_3f38856,X))) = s(V_3f38852,happ(s(fun(V_3f38856,V_3f38852),G),s(V_3f38856,X))) => s(fun(V_3f38856,V_3f38852),F) = s(fun(V_3f38856,V_3f38852),G))).
fof('h4/thm/combin/SAME_KEY_UPDATE_DIFFER_', conjecture, ![A,B,C,D]: ![F, F1, F2, A0, B0, C0]: (~ (s(D,B0) = s(D,C0)) => ~ (s(fun(C,D),'h4/const/combin/UPDATE'(s(C,A0),s(D,B0),s(fun(C,D),F))) = s(fun(C,D),'h4/const/combin/UPDATE'(s(C,A0),s(D,C0),s(fun(C,D),F)))))).
