%   ORIGINAL: 'h4/thm/pred_set/IMAGE_CONG_'
% 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 s 'f\'' 's\''. s = 's\'' /\ (!x. 'h4/const/bool/IN' x 's\'' ==> f x = 'f\'' x) ==> 'h4/const/pred_set/IMAGE' f s = 'h4/const/pred_set/IMAGE' 'f\'' '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: !f s 'f\'' 's\''. s = 's\'' /\ (!x. 'h4/const/bool/IN' x 's\'' ==> happ f x = happ 'f\'' x) ==> 'h4/const/pred_set/IMAGE' f s = 'h4/const/pred_set/IMAGE' 'f\'' '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_3f18395,V_3f18391]: ![F, G]: (![X]: s(V_3f18391,happ(s(fun(V_3f18395,V_3f18391),F),s(V_3f18395,X))) = s(V_3f18391,happ(s(fun(V_3f18395,V_3f18391),G),s(V_3f18395,X))) => s(fun(V_3f18395,V_3f18391),F) = s(fun(V_3f18395,V_3f18391),G))).
fof('h4/thm/pred_set/IMAGE_CONG_', conjecture, ![B,A]: ![F, S, V_27f_5c_27_27, V_27s_5c_27_27]: ((s(fun(A,bool),S) = s(fun(A,bool),V_27s_5c_27_27) & ![X]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),V_27s_5c_27_27)))) => s(B,happ(s(fun(A,B),F),s(A,X))) = s(B,happ(s(fun(A,B),V_27f_5c_27_27),s(A,X))))) => s(fun(B,bool),'h4/const/pred_set/IMAGE'(s(fun(A,B),F),s(fun(A,bool),S))) = s(fun(B,bool),'h4/const/pred_set/IMAGE'(s(fun(A,B),V_27f_5c_27_27),s(fun(A,bool),V_27s_5c_27_27))))).
