%   ORIGINAL: 'h4/thm/rich_list/MEM_SING_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: !d b. (!a c. ~(d = 'h4/const/list/APPEND' ('h4/const/list/APPEND' a ('h4/const/list/CONS' b 'h4/const/list/NIL')) c)) <=> ~'h4/const/bool/IN' b ('h4/const/list/LIST_TO_SET' d)
%   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: !d b. (!a c. ~(d = 'h4/const/list/APPEND' ('h4/const/list/APPEND' a ('h4/const/list/CONS' b 'h4/const/list/NIL')) c)) <=> ~'h4/const/bool/IN' b ('h4/const/list/LIST_TO_SET' d)
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_3f57836,V_3f57832]: ![F, G]: (![X]: s(V_3f57832,happ(s(fun(V_3f57836,V_3f57832),F),s(V_3f57836,X))) = s(V_3f57832,happ(s(fun(V_3f57836,V_3f57832),G),s(V_3f57836,X))) => s(fun(V_3f57836,V_3f57832),F) = s(fun(V_3f57836,V_3f57832),G))).
fof('h4/thm/rich_list/MEM_SING_APPEND_', conjecture, ![A]: ![D, B]: (![A0, C]: ~ (s('h4/type/list/list'(A),D) = 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),A0),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,B),s('h4/type/list/list'(A),'h4/const/list/NIL'))))),s('h4/type/list/list'(A),C)))) <=> ~ (p(s(bool,'h4/const/bool/IN'(s(A,B),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),D))))))))).
