Section Maps.
Context {A B : Type} {A_eq : EqDec A}.
Implicit Types (k : A) (v : B) (m : A -> option B).
Definition map_upd m k v k' := if eq_dec k' k then Some v else m k'.

Lemma map_upd_triv : forall m k v, m k = Some v -> map_upd m k v = m.