%   ORIGINAL: 'h4/thm/list/LUPDATE_SNOC_'
% 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: !ys k x y. 'h4/const/list/LUPDATE' x k ('h4/const/list/SNOC' y ys) = 'h4/const/bool/COND' (k = 'h4/const/list/LENGTH' ys) ('h4/const/list/SNOC' x ys) ('h4/const/list/SNOC' y ('h4/const/list/LUPDATE' x k ys))
%   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: !ys k x y. ?v. (v <=> k = 'h4/const/list/LENGTH' ys) /\ 'h4/const/list/LUPDATE' x k ('h4/const/list/SNOC' y ys) = 'h4/const/bool/COND' v ('h4/const/list/SNOC' x ys) ('h4/const/list/SNOC' y ('h4/const/list/LUPDATE' x k ys))
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_3f10418,V_3f10414]: ![F, G]: (![X]: s(V_3f10414,happ(s(fun(V_3f10418,V_3f10414),F),s(V_3f10418,X))) = s(V_3f10414,happ(s(fun(V_3f10418,V_3f10414),G),s(V_3f10418,X))) => s(fun(V_3f10418,V_3f10414),F) = s(fun(V_3f10418,V_3f10414),G))).
fof('h4/thm/list/LUPDATE_SNOC_', conjecture, ![A]: ![Ys, K, X, Y]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/num/num',K) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ys)))) & s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,X),s('h4/type/num/num',K),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,Y),s('h4/type/list/list'(A),Ys))))) = s('h4/type/list/list'(A),'h4/const/bool/COND'(s(bool,V),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),Ys))),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,Y),s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,X),s('h4/type/num/num',K),s('h4/type/list/list'(A),Ys))))))))).
