%   ORIGINAL: 'h4/thm/list/nub_append_'
% 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: !l1 l2. 'h4/const/list/nub' ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' ('h4/const/list/nub' ('h4/const/list/FILTER' (\x. ~'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' l2)) l1)) ('h4/const/list/nub' l2)
%   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: !_0. (!l2 x. happ (happ _0 l2) x <=> ~'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' l2)) ==> (!l1 l2. 'h4/const/list/nub' ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' ('h4/const/list/nub' ('h4/const/list/FILTER' (happ _0 l2) l1)) ('h4/const/list/nub' l2))
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_3f11394,V_3f11390]: ![F, G]: (![X]: s(V_3f11390,happ(s(fun(V_3f11394,V_3f11390),F),s(V_3f11394,X))) = s(V_3f11390,happ(s(fun(V_3f11394,V_3f11390),G),s(V_3f11394,X))) => s(fun(V_3f11394,V_3f11390),F) = s(fun(V_3f11394,V_3f11390),G))).
fof('h4/thm/list/nub_append_', conjecture, ![A]: ![V__0]: (![L2, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun('h4/type/list/list'(A),fun(A,bool)),V__0),s('h4/type/list/list'(A),L2))),s(A,X)))) <=> ~ (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L2)))))))) => ![L1, L2]: s('h4/type/list/list'(A),'h4/const/list/nub'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2))))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/nub'(s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),happ(s(fun('h4/type/list/list'(A),fun(A,bool)),V__0),s('h4/type/list/list'(A),L2))),s('h4/type/list/list'(A),L1))))),s('h4/type/list/list'(A),'h4/const/list/nub'(s('h4/type/list/list'(A),L2))))))).
