%   ORIGINAL: 'h4/thm/list/MEM_LUPDATE_'
% 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 x y i. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/LUPDATE' y i l)) <=> 'h4/const/prim_rec/<' i ('h4/const/list/LENGTH' l) /\ x = y \/ (?j. 'h4/const/prim_rec/<' j ('h4/const/list/LENGTH' l) /\ ~(i = j) /\ 'h4/const/list/EL' j l = x)
%   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 x y i. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/LUPDATE' y i l)) <=> 'h4/const/prim_rec/<' i ('h4/const/list/LENGTH' l) /\ x = y \/ (?j. 'h4/const/prim_rec/<' j ('h4/const/list/LENGTH' l) /\ ~(i = j) /\ 'h4/const/list/EL' j l = x)
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_3f10469,V_3f10465]: ![F, G]: (![X]: s(V_3f10465,happ(s(fun(V_3f10469,V_3f10465),F),s(V_3f10469,X))) = s(V_3f10465,happ(s(fun(V_3f10469,V_3f10465),G),s(V_3f10469,X))) => s(fun(V_3f10469,V_3f10465),F) = s(fun(V_3f10469,V_3f10465),G))).
fof('h4/thm/list/MEM_LUPDATE_', conjecture, ![A]: ![L, X, Y, I]: (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),'h4/const/list/LUPDATE'(s(A,Y),s('h4/type/num/num',I),s('h4/type/list/list'(A),L)))))))) <=> ((p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',I),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L)))))) & s(A,X) = s(A,Y)) | ?[J]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',J),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L)))))) & (~ (s('h4/type/num/num',I) = s('h4/type/num/num',J)) & s(A,'h4/const/list/EL'(s('h4/type/num/num',J),s('h4/type/list/list'(A),L))) = s(A,X)))))).
