Definition stream (A: Type): Type := {h: nat -> option A | forall x y, x < y -> h x = None -> h y = None}.Definition stream_get {A: Type} (h: stream A) (n: nat) := proj1_sig h n.

Lemma stream_sound1: forall {A: Type} (h: stream A) (x y: nat), x <= y -> h x = None -> h y = None.