(** Hence sqrt is a morphism *)
(** An alternate specification *)

(* Specifications: *)
Lemma sqrt_spec_alt : forall a, 0<=a -> exists r,
a == (√a)² + r /\ 0 <= r <= 2*√a.
Lemma sqrt_unique' : forall a b c, 0<=c<=2*b ->
a == b² + c -> √a == b.