%   ORIGINAL: 'h4/thm/list/LRC_MEM_right_'
% 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: !y x t h e R. 'h4/const/list/LRC' R ('h4/const/list/CONS' h t) x y /\ 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' t) ==> (?z p. R z e /\ 'h4/const/list/LRC' R p x z)
%   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: !y x t h e R. 'h4/const/list/LRC' R ('h4/const/list/CONS' h t) x y /\ 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' t) ==> (?z p. happ (happ R z) e /\ 'h4/const/list/LRC' R p x z)
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_3f7915,V_3f7911]: ![F, G]: (![X]: s(V_3f7911,happ(s(fun(V_3f7915,V_3f7911),F),s(V_3f7915,X))) = s(V_3f7911,happ(s(fun(V_3f7915,V_3f7911),G),s(V_3f7915,X))) => s(fun(V_3f7915,V_3f7911),F) = s(fun(V_3f7915,V_3f7911),G))).
fof('h4/thm/list/LRC_MEM_right_', conjecture, ![A]: ![Y, X, T, H, E, R]: ((p(s(bool,'h4/const/list/LRC'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,H),s('h4/type/list/list'(A),T))),s(A,X),s(A,Y)))) & 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),T))))))) => ?[Z, P]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,Z))),s(A,E)))) & p(s(bool,'h4/const/list/LRC'(s(fun(A,fun(A,bool)),R),s('h4/type/list/list'(A),P),s(A,X),s(A,Z))))))).
