%   ORIGINAL: 'h4/thm/bool/NOT_FORALL_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: !P. ~(!x. P x) <=> (?x. ~P x)
%   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: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
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_3f33028,V_3f33024]: ![F, G]: (![X]: s(V_3f33024,happ(s(fun(V_3f33028,V_3f33024),F),s(V_3f33028,X))) = s(V_3f33024,happ(s(fun(V_3f33028,V_3f33024),G),s(V_3f33028,X))) => s(fun(V_3f33028,V_3f33024),F) = s(fun(V_3f33028,V_3f33024),G))).
fof('h4/thm/bool/NOT_FORALL_THM_', conjecture, ![A]: ![P]: (~ (![X]: p(s(bool,happ(s(fun(A,bool),P),s(A,X))))) <=> ?[X]: ~ (p(s(bool,happ(s(fun(A,bool),P),s(A,X))))))).
