%   ORIGINAL: 'h4/thm/bool/bool_INDUCT_'
% 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. P T /\ P F ==> (!b. P 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: !P. happ P T /\ happ P F ==> (!b. happ P b)
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_3f35053,V_3f35049]: ![F, G]: (![X]: s(V_3f35049,happ(s(fun(V_3f35053,V_3f35049),F),s(V_3f35053,X))) = s(V_3f35049,happ(s(fun(V_3f35053,V_3f35049),G),s(V_3f35053,X))) => s(fun(V_3f35053,V_3f35049),F) = s(fun(V_3f35053,V_3f35049),G))).
fof('h4/thm/bool/bool_INDUCT_', conjecture, ![P]: ((p(s(bool,happ(s(fun(bool,bool),P),s(bool,'T')))) & p(s(bool,happ(s(fun(bool,bool),P),s(bool,'F'))))) => ![B]: p(s(bool,happ(s(fun(bool,bool),P),s(bool,B)))))).
