%   ORIGINAL: 'h4/thm/list/SET_TO_LIST_IND_'
% 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. (!s. ('h4/const/pred_set/FINITE' s /\ ~(s = 'h4/const/pred_set/EMPTY') ==> P ('h4/const/pred_set/REST' s)) ==> P s) ==> (!v. P v)
%   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. (!s. ('h4/const/pred_set/FINITE' s /\ ~(s = 'h4/const/pred_set/EMPTY') ==> happ P ('h4/const/pred_set/REST' s)) ==> happ P s) ==> (!v. happ P v)
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_3f8341,V_3f8337]: ![F, G]: (![X]: s(V_3f8337,happ(s(fun(V_3f8341,V_3f8337),F),s(V_3f8341,X))) = s(V_3f8337,happ(s(fun(V_3f8341,V_3f8337),G),s(V_3f8341,X))) => s(fun(V_3f8341,V_3f8337),F) = s(fun(V_3f8341,V_3f8337),G))).
fof('h4/thm/list/SET_TO_LIST_IND_', conjecture, ![A]: ![P]: (![S]: (((p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),S)))) & ~ (s(fun(A,bool),S) = s(fun(A,bool),'h4/const/pred_set/EMPTY'))) => p(s(bool,happ(s(fun(fun(A,bool),bool),P),s(fun(A,bool),'h4/const/pred_set/REST'(s(fun(A,bool),S))))))) => p(s(bool,happ(s(fun(fun(A,bool),bool),P),s(fun(A,bool),S))))) => ![V]: p(s(bool,happ(s(fun(fun(A,bool),bool),P),s(fun(A,bool),V)))))).
