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+Set Primitive Projections.
+
+CoInductive Stream : Type := Cons { tl : Stream }.
+
+Fixpoint Str_nth_tl (n:nat) (s:Stream) : Stream :=
+ match n with
+ | O => s
+ | S m => Str_nth_tl m (tl s)
+ end.
+
+CoInductive EqSt (s1 s2: Stream) : Prop := eqst {
+ eqst_tl : EqSt (tl s1) (tl s2);
+}.
+
+Axiom EqSt_reflex : forall (s : Stream), EqSt s s.
+
+CoFixpoint map (s:Stream) : Stream := Cons (map (tl s)).
+
+Lemma Str_nth_tl_map : forall n s, EqSt (Str_nth_tl n (map s)) (map (Str_nth_tl n s)).
+Proof.
+induction n.
++ intros; apply EqSt_reflex.
++ cbn; intros s; apply IHn.
+Qed.
+
+Definition boom : forall s, tl (map s) = map (tl s) := fun s => eq_refl.