%   ORIGINAL: 'h4/thm/rich_list/ASSOC_FOLDR_FLAT_'
% 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/operator/ASSOC' f ==> (!e. 'h4/const/operator/LEFT_ID' f e ==> (!l. 'h4/const/list/FOLDR' f e ('h4/const/list/FLAT' l) = 'h4/const/list/FOLDR' f e ('h4/const/list/MAP' ('h4/const/list/FOLDR' f e) l)))
%   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/operator/ASSOC' f ==> (!e. 'h4/const/operator/LEFT_ID' f e ==> (!l. happ ('h4/const/list/FOLDR' f e) ('h4/const/list/FLAT' l) = happ ('h4/const/list/FOLDR' f e) ('h4/const/list/MAP' ('h4/const/list/FOLDR' f e) l)))
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_3f52986,V_3f52982]: ![F, G]: (![X]: s(V_3f52982,happ(s(fun(V_3f52986,V_3f52982),F),s(V_3f52986,X))) = s(V_3f52982,happ(s(fun(V_3f52986,V_3f52982),G),s(V_3f52986,X))) => s(fun(V_3f52986,V_3f52982),F) = s(fun(V_3f52986,V_3f52982),G))).
fof('h4/thm/rich_list/ASSOC_FOLDR_FLAT_', conjecture, ![A]: ![F]: (p(s(bool,'h4/const/operator/ASSOC'(s(fun(A,fun(A,A)),F)))) => ![E]: (p(s(bool,'h4/const/operator/LEFT_ID'(s(fun(A,fun(A,A)),F),s(A,E)))) => ![L]: s(A,happ(s(fun('h4/type/list/list'(A),A),'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E))),s('h4/type/list/list'(A),'h4/const/list/FLAT'(s('h4/type/list/list'('h4/type/list/list'(A)),L))))) = s(A,happ(s(fun('h4/type/list/list'(A),A),'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E))),s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun('h4/type/list/list'(A),A),'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E))),s('h4/type/list/list'('h4/type/list/list'(A)),L)))))))).
