%   ORIGINAL: 'h4/thm/pred_set/PROD_IMAGE_THM_0'
% 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. 'h4/const/pred_set/PROD_IMAGE' f 'h4/const/pred_set/EMPTY' = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')
%   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. 'h4/const/pred_set/PROD_IMAGE' f 'h4/const/pred_set/EMPTY' = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')
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_3f22698,V_3f22694]: ![F, G]: (![X]: s(V_3f22694,happ(s(fun(V_3f22698,V_3f22694),F),s(V_3f22698,X))) = s(V_3f22694,happ(s(fun(V_3f22698,V_3f22694),G),s(V_3f22698,X))) => s(fun(V_3f22698,V_3f22694),F) = s(fun(V_3f22698,V_3f22694),G))).
fof('h4/thm/pred_set/PROD_IMAGE_THM_0', conjecture, ![A]: ![F]: s('h4/type/num/num','h4/const/pred_set/PROD_IMAGE'(s(fun(A,'h4/type/num/num'),F),s(fun(A,bool),'h4/const/pred_set/EMPTY'))) = s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO')))))).
