%   ORIGINAL: 'h4/thm/list/FOLDL_SNOC_'
% 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 x l. 'h4/const/list/FOLDL' f e ('h4/const/list/SNOC' x l) = f ('h4/const/list/FOLDL' f e l) x
%   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 e x l. 'h4/const/list/FOLDL' f e ('h4/const/list/SNOC' x l) = happ (happ f ('h4/const/list/FOLDL' f e l)) x
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_3f9666,V_3f9662]: ![F, G]: (![X]: s(V_3f9662,happ(s(fun(V_3f9666,V_3f9662),F),s(V_3f9666,X))) = s(V_3f9662,happ(s(fun(V_3f9666,V_3f9662),G),s(V_3f9666,X))) => s(fun(V_3f9666,V_3f9662),F) = s(fun(V_3f9666,V_3f9662),G))).
fof('h4/thm/list/FOLDL_SNOC_', conjecture, ![B,A]: ![F, E, X, L]: s(B,'h4/const/list/FOLDL'(s(fun(B,fun(A,B)),F),s(B,E),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),L))))) = s(B,happ(s(fun(A,B),happ(s(fun(B,fun(A,B)),F),s(B,'h4/const/list/FOLDL'(s(fun(B,fun(A,B)),F),s(B,E),s('h4/type/list/list'(A),L))))),s(A,X)))).
