(*+ Resource maps *)
(** In this file: - common results about lists - definition of resource maps, ignoring problems related to step indexing *)
(*+ List functions *)
Fixpoint nth {A} (l : list A) i :=
match l with
| nil => None
| x :: l =>
match i with
| O => Some x
| S i => nth l i
end
end.
Fixpoint nth_upd {A} (l : list A) i x :=
match l with
| nil => nil
| y :: l =>
match i with
| O => x :: l
| S i => y :: nth_upd l i x
end
end.
Ltac ifeq :=
match goal with
[ H : context [ eq_nat_dec ?x ?x ] |- _ ] => destruct (eq_nat_dec x x) as [_|]; [|congruence]
| [ |- context [ eq_nat_dec ?x ?x ] ] => destruct (eq_nat_dec x x) as [_|]; [|congruence]
| [ H : context [ eq_nat_dec ?x ?y ] |- _ ] => destruct (eq_nat_dec x y)
| [ |- context [ eq_nat_dec ?x ?y ] ] => destruct (eq_nat_dec x y)
end.

Lemma nth_nth_upd' {A} i j l (x : A) :
j <> i ->
nth (nth_upd l i x) j = nth l j.