%   ORIGINAL: 'h4/thm/rich_list/MEM_LAST_FRONT_'
% 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: !e l h. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) /\ ~(e = 'h4/const/list/LAST' ('h4/const/list/CONS' h l)) ==> 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' ('h4/const/list/FRONT' ('h4/const/list/CONS' h 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: !e l h. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) /\ ~(e = 'h4/const/list/LAST' ('h4/const/list/CONS' h l)) ==> 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' ('h4/const/list/FRONT' ('h4/const/list/CONS' h 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_3f57536,V_3f57532]: ![F, G]: (![X]: s(V_3f57532,happ(s(fun(V_3f57536,V_3f57532),F),s(V_3f57536,X))) = s(V_3f57532,happ(s(fun(V_3f57536,V_3f57532),G),s(V_3f57536,X))) => s(fun(V_3f57536,V_3f57532),F) = s(fun(V_3f57536,V_3f57532),G))).
fof('h4/thm/rich_list/MEM_LAST_FRONT_', conjecture, ![A]: ![E, L, H]: ((p(s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L)))))) & ~ (s(A,E) = s(A,'h4/const/list/LAST'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),L))))))) => p(s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),'h4/const/list/FRONT'(s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),L)))))))))))).
