%   ORIGINAL: 'h4/thm/res_quan/RES_SELECT_EMPTY_'
% 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_SELECT' 'h4/const/pred_set/EMPTY' p = 'h4/const/min/@' (\x. F)
%   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 <=> F) ==> (!p. 'h4/const/bool/RES_SELECT' 'h4/const/pred_set/EMPTY' p = 'h4/const/min/@' _0)
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_3f31278,V_3f31274]: ![F, G]: (![X]: s(V_3f31274,happ(s(fun(V_3f31278,V_3f31274),F),s(V_3f31278,X))) = s(V_3f31274,happ(s(fun(V_3f31278,V_3f31274),G),s(V_3f31278,X))) => s(fun(V_3f31278,V_3f31274),F) = s(fun(V_3f31278,V_3f31274),G))).
fof('h4/thm/res_quan/RES_SELECT_EMPTY_', conjecture, ![A]: ![V__0]: (![X]: s(bool,happ(s(fun(A,bool),V__0),s(A,X))) = s(bool,'F') => ![P]: s(A,'h4/const/bool/RES_SELECT'(s(fun(A,bool),'h4/const/pred_set/EMPTY'),s(fun(A,bool),P))) = s(A,'h4/const/min/@'(s(fun(A,bool),V__0))))).
