%   ORIGINAL: 'h4/thm/pred_set/CHOICE_NOT_IN_REST_'
% 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: !s. ~'h4/const/bool/IN' ('h4/const/pred_set/CHOICE' s) ('h4/const/pred_set/REST' s)
%   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: !s. ~'h4/const/bool/IN' ('h4/const/pred_set/CHOICE' s) ('h4/const/pred_set/REST' s)
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_3f17570,V_3f17566]: ![F, G]: (![X]: s(V_3f17566,happ(s(fun(V_3f17570,V_3f17566),F),s(V_3f17570,X))) = s(V_3f17566,happ(s(fun(V_3f17570,V_3f17566),G),s(V_3f17570,X))) => s(fun(V_3f17570,V_3f17566),F) = s(fun(V_3f17570,V_3f17566),G))).
fof('h4/thm/pred_set/CHOICE_NOT_IN_REST_', conjecture, ![A]: ![S]: ~ (p(s(bool,'h4/const/bool/IN'(s(A,'h4/const/pred_set/CHOICE'(s(fun(A,bool),S))),s(fun(A,bool),'h4/const/pred_set/REST'(s(fun(A,bool),S)))))))).
