%   ORIGINAL: 'h4/thm/pred_set/ITSET_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: !f P. (!s b. ('h4/const/pred_set/FINITE' s /\ ~(s = 'h4/const/pred_set/EMPTY') ==> P ('h4/const/pred_set/REST' s) (f ('h4/const/pred_set/CHOICE' s) b)) ==> P s b) ==> (!v v1. P v v1)
%   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: !f P. (!s b. ('h4/const/pred_set/FINITE' s /\ ~(s = 'h4/const/pred_set/EMPTY') ==> happ (happ P ('h4/const/pred_set/REST' s)) (happ (happ f ('h4/const/pred_set/CHOICE' s)) b)) ==> happ (happ P s) b) ==> (!v v1. happ (happ P v) v1)
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_3f21972,V_3f21968]: ![F, G]: (![X]: s(V_3f21968,happ(s(fun(V_3f21972,V_3f21968),F),s(V_3f21972,X))) = s(V_3f21968,happ(s(fun(V_3f21972,V_3f21968),G),s(V_3f21972,X))) => s(fun(V_3f21972,V_3f21968),F) = s(fun(V_3f21972,V_3f21968),G))).
fof('h4/thm/pred_set/ITSET_IND_', conjecture, ![A,B]: ![F, P]: (![S, B0]: (((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(B,bool),happ(s(fun(fun(A,bool),fun(B,bool)),P),s(fun(A,bool),'h4/const/pred_set/REST'(s(fun(A,bool),S))))),s(B,happ(s(fun(B,B),happ(s(fun(A,fun(B,B)),F),s(A,'h4/const/pred_set/CHOICE'(s(fun(A,bool),S))))),s(B,B0))))))) => p(s(bool,happ(s(fun(B,bool),happ(s(fun(fun(A,bool),fun(B,bool)),P),s(fun(A,bool),S))),s(B,B0))))) => ![V, V1]: p(s(bool,happ(s(fun(B,bool),happ(s(fun(fun(A,bool),fun(B,bool)),P),s(fun(A,bool),V))),s(B,V1)))))).
