%   ORIGINAL: 'h4/thm/list/MAP_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: !l f. 'h4/const/list/MAP' f ('h4/const/list/FLAT' l) = 'h4/const/list/FLAT' ('h4/const/list/MAP' ('h4/const/list/MAP' f) 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: !l f. happ ('h4/const/list/MAP' f) ('h4/const/list/FLAT' l) = 'h4/const/list/FLAT' (happ ('h4/const/list/MAP' ('h4/const/list/MAP' f)) 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_3f11094,V_3f11090]: ![F, G]: (![X]: s(V_3f11090,happ(s(fun(V_3f11094,V_3f11090),F),s(V_3f11094,X))) = s(V_3f11090,happ(s(fun(V_3f11094,V_3f11090),G),s(V_3f11094,X))) => s(fun(V_3f11094,V_3f11090),F) = s(fun(V_3f11094,V_3f11090),G))).
fof('h4/thm/list/MAP_FLAT_', conjecture, ![A,B]: ![L, F]: s('h4/type/list/list'(A),happ(s(fun('h4/type/list/list'(B),'h4/type/list/list'(A)),'h4/const/list/MAP'(s(fun(B,A),F))),s('h4/type/list/list'(B),'h4/const/list/FLAT'(s('h4/type/list/list'('h4/type/list/list'(B)),L))))) = s('h4/type/list/list'(A),'h4/const/list/FLAT'(s('h4/type/list/list'('h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'('h4/type/list/list'(B)),'h4/type/list/list'('h4/type/list/list'(A))),'h4/const/list/MAP'(s(fun('h4/type/list/list'(B),'h4/type/list/list'(A)),'h4/const/list/MAP'(s(fun(B,A),F))))),s('h4/type/list/list'('h4/type/list/list'(B)),L)))))).
