(** This file defines complex numbers [C] as [R * R]. Operations are
given, and [C] is proved to be a field, a normed module, and a
complete space. *)

(** * The set of complex numbers *)

Definition C := (R * R)%type.Definition RtoC (x : R) : C := (x,0).

(* Specifications: *)
Lemma RtoC_inj : forall (x y : R), RtoC x = RtoC y -> x = y.
Lemma Ceq_dec (z1 z2 : C) : { z1 = z2 } + { z1 <> z2 }.