%   ORIGINAL: 'h4/thm/list/LUPDATE_compute_2'
% 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 n x l. 'h4/const/list/LUPDATE' e ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/list/CONS' x l) = 'h4/const/list/CONS' x ('h4/const/list/LUPDATE' e ('h4/const/arithmetic/-' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 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 n x l. 'h4/const/list/LUPDATE' e ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/list/CONS' x l) = 'h4/const/list/CONS' x ('h4/const/list/LUPDATE' e ('h4/const/arithmetic/-' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' n)) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 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_3f10544,V_3f10540]: ![F, G]: (![X]: s(V_3f10540,happ(s(fun(V_3f10544,V_3f10540),F),s(V_3f10544,X))) = s(V_3f10540,happ(s(fun(V_3f10544,V_3f10540),G),s(V_3f10544,X))) => s(fun(V_3f10544,V_3f10540),F) = s(fun(V_3f10544,V_3f10540),G))).
fof('h4/thm/list/LUPDATE_compute_2', conjecture, ![A]: ![E, N, X, L]: s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,E),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num',N))))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X),s('h4/type/list/list'(A),L))))) = s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X),s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,E),s('h4/type/num/num','h4/const/arithmetic/-'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num',N))))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))),s('h4/type/list/list'(A),L)))))).
