%   ORIGINAL: 'h4/thm/rich_list/NULL_FOLDL_'
% 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/NULL' l <=> 'h4/const/list/FOLDL' (\x 'l\''. F) T 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. (!'l\''. happ _1 'l\'' <=> F) ==> (!_0. (!x. happ _0 x = _1) ==> (!l. 'h4/const/list/NULL' l <=> 'h4/const/list/FOLDL' _0 T 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_3f53186,V_3f53182]: ![F, G]: (![X]: s(V_3f53182,happ(s(fun(V_3f53186,V_3f53182),F),s(V_3f53186,X))) = s(V_3f53182,happ(s(fun(V_3f53186,V_3f53182),G),s(V_3f53186,X))) => s(fun(V_3f53186,V_3f53182),F) = s(fun(V_3f53186,V_3f53182),G))).
fof('h4/thm/rich_list/NULL_FOLDL_', conjecture, ![A]: ![V__1]: (![V_27l_5c_27_27]: s(bool,happ(s(fun(A,bool),V__1),s(A,V_27l_5c_27_27))) = s(bool,'F') => ![V__0]: (![X]: s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),V__0),s(bool,X))) = s(fun(A,bool),V__1) => ![L]: s(bool,'h4/const/list/NULL'(s('h4/type/list/list'(A),L))) = s(bool,'h4/const/list/FOLDL'(s(fun(bool,fun(A,bool)),V__0),s(bool,'T'),s('h4/type/list/list'(A),L)))))).
