%   ORIGINAL: 'h4/thm/quotient_list/FILTER_PRS_'
% 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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!P l. 'h4/const/list/FILTER' P l = 'h4/const/list/MAP' abs ('h4/const/list/FILTER' ('h4/const/quotient/-->' abs 'h4/const/combin/I' P) ('h4/const/list/MAP' rep 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: !R abs rep. 'h4/const/quotient/QUOTIENT' R abs rep ==> (!P l. 'h4/const/list/FILTER' P l = 'h4/const/list/MAP' abs ('h4/const/list/FILTER' ('h4/const/quotient/-->' abs 'h4/const/combin/I' P) ('h4/const/list/MAP' rep 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_3f67761,V_3f67757]: ![F, G]: (![X]: s(V_3f67757,happ(s(fun(V_3f67761,V_3f67757),F),s(V_3f67761,X))) = s(V_3f67757,happ(s(fun(V_3f67761,V_3f67757),G),s(V_3f67761,X))) => s(fun(V_3f67761,V_3f67757),F) = s(fun(V_3f67761,V_3f67757),G))).
fof('h4/thm/quotient_list/FILTER_PRS_', conjecture, ![A,B]: ![R, Abs, Rep]: (p(s(bool,'h4/const/quotient/QUOTIENT'(s(fun(A,fun(A,bool)),R),s(fun(A,B),Abs),s(fun(B,A),Rep)))) => ![P, L]: s('h4/type/list/list'(B),'h4/const/list/FILTER'(s(fun(B,bool),P),s('h4/type/list/list'(B),L))) = s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),Abs),s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),'h4/const/quotient/-->'(s(fun(A,B),Abs),s(fun(bool,bool),'h4/const/combin/I'),s(fun(B,bool),P))),s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun(B,A),Rep),s('h4/type/list/list'(B),L))))))))).
