%   ORIGINAL: 'h4/thm/bool/RES_FORALL_TRUE_'
% 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. 'h4/const/bool/RES_FORALL' P (\x. T) <=> T
%   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. (!x. happ _0 x <=> T) ==> (!P. 'h4/const/bool/RES_FORALL' P _0 <=> T)
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_3f35278,V_3f35274]: ![F, G]: (![X]: s(V_3f35274,happ(s(fun(V_3f35278,V_3f35274),F),s(V_3f35278,X))) = s(V_3f35274,happ(s(fun(V_3f35278,V_3f35274),G),s(V_3f35278,X))) => s(fun(V_3f35278,V_3f35274),F) = s(fun(V_3f35278,V_3f35274),G))).
fof('h4/thm/bool/RES_FORALL_TRUE_', conjecture, ![A]: ![V__0]: (![X]: s(bool,happ(s(fun(A,bool),V__0),s(A,X))) = s(bool,'T') => ![P]: s(bool,'h4/const/bool/RES_FORALL'(s(fun(A,bool),P),s(fun(A,bool),V__0))) = s(bool,'T'))).
