%   ORIGINAL: 'h4/thm/rich_list/EVERY_FOLDR_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: !P l. 'h4/const/list/EVERY' P l <=> 'h4/const/list/FOLDR' $and T ('h4/const/list/MAP' P 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: !P l. 'h4/const/list/EVERY' P l <=> 'h4/const/list/FOLDR' $and T ('h4/const/list/MAP' P l)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f52836,V_3f52832]: ![F, G]: (![X]: s(V_3f52832,happ(s(fun(V_3f52836,V_3f52832),F),s(V_3f52836,X))) = s(V_3f52832,happ(s(fun(V_3f52836,V_3f52832),G),s(V_3f52836,X))) => s(fun(V_3f52836,V_3f52832),F) = s(fun(V_3f52836,V_3f52832),G))).
fof('h4/thm/rich_list/EVERY_FOLDR_MAP_', conjecture, ![A]: ![P, L]: s(bool,'h4/const/list/EVERY'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))) = s(bool,'h4/const/list/FOLDR'(s(fun(bool,fun(bool,bool)),'$and'),s(bool,'T'),s('h4/type/list/list'(bool),'h4/const/list/MAP'(s(fun(A,bool),P),s('h4/type/list/list'(A),L)))))).
