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_concat: forall G F E x A, binds x (Tm A) (F ++ E ++ G) <-> binds x (Tm A) (F) \/ binds x (Tm A) (E) \/ binds x (Tm A) (G).