%   ORIGINAL: 'h4/thm/rich_list/FOLDL_SNOC_NIL_'
% 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. 'h4/const/list/FOLDL' (\xs x. 'h4/const/list/SNOC' x xs) 'h4/const/list/NIL' l = 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. (!xs x. happ (happ _1 xs) x = 'h4/const/list/SNOC' x xs) ==> (!_0. (!xs. happ _0 xs = happ _1 xs) ==> (!l. 'h4/const/list/FOLDL' _0 'h4/const/list/NIL' l = 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_3f52561,V_3f52557]: ![F, G]: (![X]: s(V_3f52557,happ(s(fun(V_3f52561,V_3f52557),F),s(V_3f52561,X))) = s(V_3f52557,happ(s(fun(V_3f52561,V_3f52557),G),s(V_3f52561,X))) => s(fun(V_3f52561,V_3f52557),F) = s(fun(V_3f52561,V_3f52557),G))).
fof('h4/thm/rich_list/FOLDL_SNOC_NIL_', conjecture, ![A]: ![V__1]: (![Xs, X]: s('h4/type/list/list'(A),happ(s(fun(A,'h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'(A),fun(A,'h4/type/list/list'(A))),V__1),s('h4/type/list/list'(A),Xs))),s(A,X))) = s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),Xs))) => ![V__0]: (![Xs]: s(fun(A,'h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'(A),fun(A,'h4/type/list/list'(A))),V__0),s('h4/type/list/list'(A),Xs))) = s(fun(A,'h4/type/list/list'(A)),happ(s(fun('h4/type/list/list'(A),fun(A,'h4/type/list/list'(A))),V__1),s('h4/type/list/list'(A),Xs))) => ![L]: s('h4/type/list/list'(A),'h4/const/list/FOLDL'(s(fun('h4/type/list/list'(A),fun(A,'h4/type/list/list'(A))),V__0),s('h4/type/list/list'(A),'h4/const/list/NIL'),s('h4/type/list/list'(A),L))) = s('h4/type/list/list'(A),L)))).
