%   ORIGINAL: 'h4/thm/list/EVERY2_LUPDATE_same_'
% 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: !P l1 l2 v1 v2 n. P v1 v2 /\ 'h4/const/list/LIST_REL' P l1 l2 ==> 'h4/const/list/LIST_REL' P ('h4/const/list/LUPDATE' v1 n l1) ('h4/const/list/LUPDATE' v2 n l2)
%   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: !P l1 l2 v1 v2 n. happ (happ P v1) v2 /\ 'h4/const/list/LIST_REL' P l1 l2 ==> 'h4/const/list/LIST_REL' P ('h4/const/list/LUPDATE' v1 n l1) ('h4/const/list/LUPDATE' v2 n l2)
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_3f11744,V_3f11740]: ![F, G]: (![X]: s(V_3f11740,happ(s(fun(V_3f11744,V_3f11740),F),s(V_3f11744,X))) = s(V_3f11740,happ(s(fun(V_3f11744,V_3f11740),G),s(V_3f11744,X))) => s(fun(V_3f11744,V_3f11740),F) = s(fun(V_3f11744,V_3f11740),G))).
fof('h4/thm/list/EVERY2_LUPDATE_same_', conjecture, ![A,B]: ![P, L1, L2, V1, V2, N]: ((p(s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,V1))),s(B,V2)))) & p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),P),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))))) => p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),P),s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,V1),s('h4/type/num/num',N),s('h4/type/list/list'(A),L1))),s('h4/type/list/list'(B),'h4/const/list/LUPDATE'(s(B,V2),s('h4/type/num/num',N),s('h4/type/list/list'(B),L2)))))))).
