+
+corec theorem nstream_eq_inv_ext: ∀f1,f2. (∀i. f1@❴i❵ = f2@❴i❵) → f1 ≗ f2.
+* #n1 #f1 * #n2 #f2 #Hf @eq_seq
+[ @(Hf 0)
+| @nstream_eq_inv_ext -nstream_eq_inv_ext #i
+ lapply (Hf 0) >apply_O1 >apply_O1 #H destruct
+ lapply (Hf (↑i)) >apply_S1 >apply_S1 #H
+ /3 width=2 by injective_plus_r, injective_S/
+]
+qed-.