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Module Type SIG.
  Inductive w : Set :=
      A : w.
  Parameter f : w -> w.
End SIG.

Module M : SIG.
  Inductive w : Set :=
      A : w.
  Definition f x := match x with
                    | A => A
                    end.
End M.

Module N := M.

Check (N.f M.A).