%   ORIGINAL: 'h4/thm/combin/UPD11_SAME_BASE_'
% 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 a b c d. 'h4/const/combin/UPDATE' a c f = 'h4/const/combin/UPDATE' b d f <=> a = b /\ c = d \/ ~(a = b) /\ 'h4/const/combin/UPDATE' a c f = f /\ 'h4/const/combin/UPDATE' b d f = 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 a b c d. 'h4/const/combin/UPDATE' a c f = 'h4/const/combin/UPDATE' b d f <=> a = b /\ c = d \/ ~(a = b) /\ 'h4/const/combin/UPDATE' a c f = f /\ 'h4/const/combin/UPDATE' b d f = 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_3f38831,V_3f38827]: ![F, G]: (![X]: s(V_3f38827,happ(s(fun(V_3f38831,V_3f38827),F),s(V_3f38831,X))) = s(V_3f38827,happ(s(fun(V_3f38831,V_3f38827),G),s(V_3f38831,X))) => s(fun(V_3f38831,V_3f38827),F) = s(fun(V_3f38831,V_3f38827),G))).
fof('h4/thm/combin/UPD11_SAME_BASE_', conjecture, ![A,B]: ![F, A0, B0, C, D]: (s(fun(A,B),'h4/const/combin/UPDATE'(s(A,A0),s(B,C),s(fun(A,B),F))) = s(fun(A,B),'h4/const/combin/UPDATE'(s(A,B0),s(B,D),s(fun(A,B),F))) <=> ((s(A,A0) = s(A,B0) & s(B,C) = s(B,D)) | (~ (s(A,A0) = s(A,B0)) & (s(fun(A,B),'h4/const/combin/UPDATE'(s(A,A0),s(B,C),s(fun(A,B),F))) = s(fun(A,B),F) & s(fun(A,B),'h4/const/combin/UPDATE'(s(A,B0),s(B,D),s(fun(A,B),F))) = s(fun(A,B),F)))))).
