%   ORIGINAL: 'h4/thm/list/FOLDL2_def_0'
% 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 cs c bs b a. 'h4/const/list/FOLDL2' f a ('h4/const/list/CONS' b bs) ('h4/const/list/CONS' c cs) = 'h4/const/list/FOLDL2' f (f a b c) bs cs
%   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 cs c bs b a. 'h4/const/list/FOLDL2' f a ('h4/const/list/CONS' b bs) ('h4/const/list/CONS' c cs) = 'h4/const/list/FOLDL2' f (happ (happ (happ f a) b) c) bs cs
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_3f7365,V_3f7361]: ![F, G]: (![X]: s(V_3f7361,happ(s(fun(V_3f7365,V_3f7361),F),s(V_3f7365,X))) = s(V_3f7361,happ(s(fun(V_3f7365,V_3f7361),G),s(V_3f7365,X))) => s(fun(V_3f7365,V_3f7361),F) = s(fun(V_3f7365,V_3f7361),G))).
fof('h4/thm/list/FOLDL2_def_0', conjecture, ![A,B,C]: ![F, Cs, C0, Bs, B0, A0]: s(A,'h4/const/list/FOLDL2'(s(fun(A,fun(B,fun(C,A))),F),s(A,A0),s('h4/type/list/list'(B),'h4/const/list/CONS'(s(B,B0),s('h4/type/list/list'(B),Bs))),s('h4/type/list/list'(C),'h4/const/list/CONS'(s(C,C0),s('h4/type/list/list'(C),Cs))))) = s(A,'h4/const/list/FOLDL2'(s(fun(A,fun(B,fun(C,A))),F),s(A,happ(s(fun(C,A),happ(s(fun(B,fun(C,A)),happ(s(fun(A,fun(B,fun(C,A))),F),s(A,A0))),s(B,B0))),s(C,C0))),s('h4/type/list/list'(B),Bs),s('h4/type/list/list'(C),Cs)))).
