%   ORIGINAL: 'h4/thm/combin/APPLY_UPDATE_THM_'
% 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. 'h4/const/combin/UPDATE' a b f c = 'h4/const/bool/COND' (a = c) b (f c)
%   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. ?v. (v <=> a = c) /\ 'h4/const/combin/UPDATE' a b f c = 'h4/const/bool/COND' v b (happ f c)
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_3f38680,V_3f38676]: ![F, G]: (![X]: s(V_3f38676,happ(s(fun(V_3f38680,V_3f38676),F),s(V_3f38680,X))) = s(V_3f38676,happ(s(fun(V_3f38680,V_3f38676),G),s(V_3f38680,X))) => s(fun(V_3f38680,V_3f38676),F) = s(fun(V_3f38680,V_3f38676),G))).
fof('h4/thm/combin/APPLY_UPDATE_THM_', conjecture, ![B,A]: ![F, A0, B0, C]: ?[V]: ((p(s(bool,V)) <=> s(A,A0) = s(A,C)) & s(B,'h4/const/combin/UPDATE'(s(A,A0),s(B,B0),s(fun(A,B),F),s(A,C))) = s(B,'h4/const/bool/COND'(s(bool,V),s(B,B0),s(B,happ(s(fun(A,B),F),s(A,C))))))).
