%   ORIGINAL: 'h4/thm/pred_set/IMAGE_BIGUNION_'
% 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 M. 'h4/const/pred_set/IMAGE' f ('h4/const/pred_set/BIGUNION' M) = 'h4/const/pred_set/BIGUNION' ('h4/const/pred_set/IMAGE' ('h4/const/pred_set/IMAGE' f) M)
%   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 M. happ ('h4/const/pred_set/IMAGE' f) ('h4/const/pred_set/BIGUNION' M) = 'h4/const/pred_set/BIGUNION' (happ ('h4/const/pred_set/IMAGE' ('h4/const/pred_set/IMAGE' f)) M)
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_3f24903,V_3f24899]: ![F, G]: (![X]: s(V_3f24899,happ(s(fun(V_3f24903,V_3f24899),F),s(V_3f24903,X))) = s(V_3f24899,happ(s(fun(V_3f24903,V_3f24899),G),s(V_3f24903,X))) => s(fun(V_3f24903,V_3f24899),F) = s(fun(V_3f24903,V_3f24899),G))).
fof('h4/thm/pred_set/IMAGE_BIGUNION_', conjecture, ![B,A]: ![F, M]: s(fun(B,bool),happ(s(fun(fun(A,bool),fun(B,bool)),'h4/const/pred_set/IMAGE'(s(fun(A,B),F))),s(fun(A,bool),'h4/const/pred_set/BIGUNION'(s(fun(fun(A,bool),bool),M))))) = s(fun(B,bool),'h4/const/pred_set/BIGUNION'(s(fun(fun(B,bool),bool),happ(s(fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool)),'h4/const/pred_set/IMAGE'(s(fun(fun(A,bool),fun(B,bool)),'h4/const/pred_set/IMAGE'(s(fun(A,B),F))))),s(fun(fun(A,bool),bool),M)))))).
