%   ORIGINAL: 'h4/thm/bool/EXISTS_UNIQUE_REFL_'
% 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. 'h4/const/bool/?!' (\x. x = a)
%   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: !_0. (!a x. happ (happ _0 a) x <=> x = a) ==> (!a. 'h4/const/bool/?!' (happ _0 a))
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_3f34803,V_3f34799]: ![F, G]: (![X]: s(V_3f34799,happ(s(fun(V_3f34803,V_3f34799),F),s(V_3f34803,X))) = s(V_3f34799,happ(s(fun(V_3f34803,V_3f34799),G),s(V_3f34803,X))) => s(fun(V_3f34803,V_3f34799),F) = s(fun(V_3f34803,V_3f34799),G))).
fof('h4/thm/bool/EXISTS_UNIQUE_REFL_', conjecture, ![A]: ![V__0]: (![A0, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),V__0),s(A,A0))),s(A,X)))) <=> s(A,X) = s(A,A0)) => ![A0]: p(s(bool,'h4/const/bool/?!'(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),V__0),s(A,A0)))))))).
