Module Type NZSqrtProp
(Import A : NZOrdAxiomsSig')
(Import B : NZSqrt' A)
(Import C : NZMulOrderProp A).
Local Notation "a ²" := (a*a) (at level 5, no associativity, format "a ²").
(** First, sqrt is non-negative *)
(** The spec of sqrt indeed determines it *)

Lemma sqrt_unique : forall a b, b² <= a < (S b)² -> √a == b.