(** Extensional Equality between two streams  *)

CoInductive EqSt (s1 s2: Stream) : Prop :=
    eqst :
        hd s1 = hd s2 -> EqSt (tl s1) (tl s2) -> EqSt s1 s2.(** Extensional Equality between two streams  *)

CoInductive EqSt (s1 s2: Stream) : Prop :=
    eqst :
        hd s1 = hd s2 -> EqSt (tl s1) (tl s2) -> EqSt s1 s2.(** A coinduction principle *)

Ltac coinduction proof :=
  cofix proof; intros; constructor;
   [ clear proof | try (apply proof; clear proof) ].

Theorem trans_EqSt : forall s1 s2 s3:Stream, EqSt s1 s2 -> EqSt s2 s3 -> EqSt s1 s3.