%   ORIGINAL: 'h4/thm/bool/BOOL_FUN_CASES_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. f = (\b. T) \/ f = (\b. F) \/ f = (\b. b) \/ f = (\b. ~b)
%   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. (!x. happ f x <=> T) \/ (!x. happ f x <=> F) \/ (!x. happ f x <=> x) \/ (!x. happ f x <=> ~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_3f35328,V_3f35324]: ![F, G]: (![X]: s(V_3f35324,happ(s(fun(V_3f35328,V_3f35324),F),s(V_3f35328,X))) = s(V_3f35324,happ(s(fun(V_3f35328,V_3f35324),G),s(V_3f35328,X))) => s(fun(V_3f35328,V_3f35324),F) = s(fun(V_3f35328,V_3f35324),G))).
fof('h4/thm/bool/BOOL_FUN_CASES_THM_', conjecture, ![F]: (![X]: s(bool,happ(s(fun(bool,bool),F),s(bool,X))) = s(bool,'T') | (![X]: s(bool,happ(s(fun(bool,bool),F),s(bool,X))) = s(bool,'F') | (![X]: s(bool,happ(s(fun(bool,bool),F),s(bool,X))) = s(bool,X) | ![X]: (p(s(bool,happ(s(fun(bool,bool),F),s(bool,X)))) <=> ~ (p(s(bool,X)))))))).
