%   ORIGINAL: 'h4/thm/rich_list/FOLDL_MAP_'
% 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 e g l. 'h4/const/list/FOLDL' f e ('h4/const/list/MAP' g l) = 'h4/const/list/FOLDL' (\x y. f x (g y)) 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: !_1. (!f x g y. happ (happ (happ (happ _1 f) x) g) y = happ (happ f x) (happ g y)) ==> (!_0. (!f g x. happ (happ (happ _0 f) g) x = happ (happ (happ _1 f) x) g) ==> (!f e g l. 'h4/const/list/FOLDL' f e ('h4/const/list/MAP' g l) = 'h4/const/list/FOLDL' (happ (happ _0 f) g) 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_3f52711,V_3f52707]: ![F, G]: (![X]: s(V_3f52707,happ(s(fun(V_3f52711,V_3f52707),F),s(V_3f52711,X))) = s(V_3f52707,happ(s(fun(V_3f52711,V_3f52707),G),s(V_3f52711,X))) => s(fun(V_3f52711,V_3f52707),F) = s(fun(V_3f52711,V_3f52707),G))).
fof('h4/thm/rich_list/FOLDL_MAP_', conjecture, ![B,A,C]: ![V__1]: (![F, X, G, Y]: s(A,happ(s(fun(C,A),happ(s(fun(fun(C,B),fun(C,A)),happ(s(fun(A,fun(fun(C,B),fun(C,A))),happ(s(fun(fun(A,fun(B,A)),fun(A,fun(fun(C,B),fun(C,A)))),V__1),s(fun(A,fun(B,A)),F))),s(A,X))),s(fun(C,B),G))),s(C,Y))) = s(A,happ(s(fun(B,A),happ(s(fun(A,fun(B,A)),F),s(A,X))),s(B,happ(s(fun(C,B),G),s(C,Y))))) => ![V__0]: (![F, G, X]: s(fun(C,A),happ(s(fun(A,fun(C,A)),happ(s(fun(fun(C,B),fun(A,fun(C,A))),happ(s(fun(fun(A,fun(B,A)),fun(fun(C,B),fun(A,fun(C,A)))),V__0),s(fun(A,fun(B,A)),F))),s(fun(C,B),G))),s(A,X))) = s(fun(C,A),happ(s(fun(fun(C,B),fun(C,A)),happ(s(fun(A,fun(fun(C,B),fun(C,A))),happ(s(fun(fun(A,fun(B,A)),fun(A,fun(fun(C,B),fun(C,A)))),V__1),s(fun(A,fun(B,A)),F))),s(A,X))),s(fun(C,B),G))) => ![F, E, G, L]: s(A,'h4/const/list/FOLDL'(s(fun(A,fun(B,A)),F),s(A,E),s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(C,B),G),s('h4/type/list/list'(C),L))))) = s(A,'h4/const/list/FOLDL'(s(fun(A,fun(C,A)),happ(s(fun(fun(C,B),fun(A,fun(C,A))),happ(s(fun(fun(A,fun(B,A)),fun(fun(C,B),fun(A,fun(C,A)))),V__0),s(fun(A,fun(B,A)),F))),s(fun(C,B),G))),s(A,E),s('h4/type/list/list'(C),L)))))).
