%   ORIGINAL: 'h4/thm/list/MEM_SPLIT_APPEND_last_'
% 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: !l e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) <=> (?pfx sfx. l = 'h4/const/list/APPEND' ('h4/const/list/APPEND' pfx ('h4/const/list/CONS' e 'h4/const/list/NIL')) sfx /\ ~'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' sfx))
%   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: !l e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) <=> (?pfx sfx. l = 'h4/const/list/APPEND' ('h4/const/list/APPEND' pfx ('h4/const/list/CONS' e 'h4/const/list/NIL')) sfx /\ ~'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' sfx))
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_3f10191,V_3f10187]: ![F, G]: (![X]: s(V_3f10187,happ(s(fun(V_3f10191,V_3f10187),F),s(V_3f10191,X))) = s(V_3f10187,happ(s(fun(V_3f10191,V_3f10187),G),s(V_3f10191,X))) => s(fun(V_3f10191,V_3f10187),F) = s(fun(V_3f10191,V_3f10187),G))).
fof('h4/thm/list/MEM_SPLIT_APPEND_last_', conjecture, ![A]: ![L, E]: (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)))))) <=> ?[Pfx, Sfx]: (s('h4/type/list/list'(A),L) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),Pfx),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,E),s('h4/type/list/list'(A),'h4/const/list/NIL'))))),s('h4/type/list/list'(A),Sfx))) & ~ (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),Sfx)))))))))).
