(* Basic properties *********************************************************)
-let corec eq_stream_refl: ∀A. reflexive … (eq_stream A) ≝ ?.
+corec lemma eq_stream_refl: ∀A. reflexive … (eq_stream A).
#A * #b #t @eq_seq //
qed.
-let corec eq_stream_sym: ∀A. symmetric … (eq_stream A) ≝ ?.
+corec lemma eq_stream_sym: ∀A. symmetric … (eq_stream A).
#A #t1 #t2 * -t1 -t2
#t1 #t2 #b1 #b2 #Hb #Ht @eq_seq /2 width=1 by/
qed-.
(* Main properties **********************************************************)
-let corec eq_stream_trans: ∀A. Transitive … (eq_stream A) ≝ ?.
+corec theorem eq_stream_trans: ∀A. Transitive … (eq_stream A).
#A #t1 #t * -t1 -t
#t1 #t #b1 #b * #Ht1 * #b2 #t2 #H cases (eq_stream_inv_seq A … H) -H -b
/3 width=7 by eq_seq/