%   ORIGINAL: 'h4/thm/rich_list/MAP_FILTER_'
% 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 P l. (!x. P (f x) <=> P x) ==> 'h4/const/list/MAP' f ('h4/const/list/FILTER' P l) = 'h4/const/list/FILTER' P ('h4/const/list/MAP' f 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: !f P l. (!x. happ P (happ f x) <=> happ P x) ==> 'h4/const/list/MAP' f ('h4/const/list/FILTER' P l) = 'h4/const/list/FILTER' P ('h4/const/list/MAP' f 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_3f55311,V_3f55307]: ![F, G]: (![X]: s(V_3f55307,happ(s(fun(V_3f55311,V_3f55307),F),s(V_3f55311,X))) = s(V_3f55307,happ(s(fun(V_3f55311,V_3f55307),G),s(V_3f55311,X))) => s(fun(V_3f55311,V_3f55307),F) = s(fun(V_3f55311,V_3f55307),G))).
fof('h4/thm/rich_list/MAP_FILTER_', conjecture, ![A]: ![F, P, L]: (![X]: s(bool,happ(s(fun(A,bool),P),s(A,happ(s(fun(A,A),F),s(A,X))))) = s(bool,happ(s(fun(A,bool),P),s(A,X))) => s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun(A,A),F),s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))))) = s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),P),s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun(A,A),F),s('h4/type/list/list'(A),L))))))).
