Section Sequences.
Variable n0 : nat.  (* numerical parameter for take, drop et al *)
Variable T : Type.  (* must come before the implicit Type     *)
Variable x0 : T.    (* default for head/nth *)
Implicit Types x y z : T.
Implicit Types m n : nat.
Implicit Type s : seq T.
Fixpoint size s := if s is _ :: s' then (size s').+1 else 0.

Lemma size0nil s : size s = 0 -> s = [::]. Proof. by case: s. Qed.