%   ORIGINAL: 'h4/thm/list/FOLDL_UNION_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 ls s. 'h4/const/list/FOLDL' (\s0 x. 'h4/const/pred_set/UNION' s0 (f x)) s ls = 'h4/const/pred_set/UNION' s ('h4/const/pred_set/BIGUNION' ('h4/const/pred_set/IMAGE' f ('h4/const/list/LIST_TO_SET' ls)))
%   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: !_1. (!s0 f x. happ (happ (happ _1 s0) f) x = 'h4/const/pred_set/UNION' s0 (happ f x)) ==> (!_0. (!f s0. happ (happ _0 f) s0 = happ (happ _1 s0) f) ==> (!f ls s. 'h4/const/list/FOLDL' (happ _0 f) s ls = 'h4/const/pred_set/UNION' s ('h4/const/pred_set/BIGUNION' ('h4/const/pred_set/IMAGE' f ('h4/const/list/LIST_TO_SET' ls)))))
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_3f9841,V_3f9837]: ![F, G]: (![X]: s(V_3f9837,happ(s(fun(V_3f9841,V_3f9837),F),s(V_3f9841,X))) = s(V_3f9837,happ(s(fun(V_3f9841,V_3f9837),G),s(V_3f9841,X))) => s(fun(V_3f9841,V_3f9837),F) = s(fun(V_3f9841,V_3f9837),G))).
fof('h4/thm/list/FOLDL_UNION_BIGUNION_', conjecture, ![B,A]: ![V__1]: (![S0, F, X]: s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),happ(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),V__1),s(fun(B,bool),S0))),s(fun(A,fun(B,bool)),F))),s(A,X))) = s(fun(B,bool),'h4/const/pred_set/UNION'(s(fun(B,bool),S0),s(fun(B,bool),happ(s(fun(A,fun(B,bool)),F),s(A,X))))) => ![V__0]: (![F, S0]: s(fun(A,fun(B,bool)),happ(s(fun(fun(B,bool),fun(A,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),fun(A,fun(B,bool)))),V__0),s(fun(A,fun(B,bool)),F))),s(fun(B,bool),S0))) = s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),happ(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),V__1),s(fun(B,bool),S0))),s(fun(A,fun(B,bool)),F))) => ![F, Ls, S]: s(fun(B,bool),'h4/const/list/FOLDL'(s(fun(fun(B,bool),fun(A,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),fun(A,fun(B,bool)))),V__0),s(fun(A,fun(B,bool)),F))),s(fun(B,bool),S),s('h4/type/list/list'(A),Ls))) = s(fun(B,bool),'h4/const/pred_set/UNION'(s(fun(B,bool),S),s(fun(B,bool),'h4/const/pred_set/BIGUNION'(s(fun(fun(B,bool),bool),'h4/const/pred_set/IMAGE'(s(fun(A,fun(B,bool)),F),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),Ls)))))))))))).
