-lemma tls_eq_repl (A) (n): eq_stream_repl A (λt1,t2. ⫰*[n] t1 ≗ ⫰*[n] t2).
-#A #n elim n -n //
-#n #IH * #n1 #t1 * #n2 #t2 #H elim (eq_stream_inv_seq … H) /2 width=7 by/
+lemma stream_tls_swap (A) (n) (t):
+ (⫰*[n]⫰t) = ⫰*{A}[↑n]t.
+// qed.
+
+lemma stream_tls_eq_repl (A) (n):
+ stream_eq_repl A (λt1,t2. ⫰*[n] t1 ≗ ⫰*[n] t2).
+#A #n @(nat_ind_succ … n) -n //
+#n #IH * #n1 #t1 * #n2 #t2 #H elim (stream_eq_inv_cons … H) /2 width=7 by/