Module Import Private_NZSqrt := Nop <+ NZSqrtProp A A B.Ltac auto' := trivial; try rewrite <- neq_0_lt_0; auto using le_0_l.Ltac wrap l := intros; apply l; auto'.

Lemma sqrt_spec' : forall a, √a*√a <= a < S (√a) * S (√a).