Definition first :=
  fun (A B C D  E: Prop) (p : A /\ B /\ C /\ D /\ E) =>
    match p with
      | conj H _ => H
    end.Definition second :=
  fun (A B C D E : Prop) (p : A /\ B /\ C /\ D /\ E) =>
    match p with
      | conj _ (conj H _) => H
    end.Definition third :=
  fun (A B C D E : Prop) (p : A /\ B /\ C /\ D /\ E) =>
    match p with
      | conj _ (conj _ (conj H _)) => H
    end.Definition fourth :=
  fun (A B C D E : Prop) (p : A /\ B /\ C /\ D /\ E) =>
    match p with
      | conj _ (conj _ (conj _ (conj H _))) => H
    end.Definition fifth :=
  fun (A B C D E : Prop) (p : A /\ B /\ C /\ D /\ E) =>
    match p with
      | conj _ (conj _ (conj _ (conj _ H))) => H
    end.

Lemma binds_map_3 : forall a b x s (f : a -> b) G, binds x s (map f G) -> exists s', f s' = s /\ binds x s' G.