Definition F (A : Set) (f : ad -> A -> M) (r : ad * A) 
  (m : M) := let (a, y) := r in op (f a y) m.

Lemma my_alist_of_map_lemma_1 : forall (A : Set) (m : Map A) (a : ad) (y : A), MapGet _ m a = Some y -> In (a, y) (alist_of_Map _ m).