Definition Zmax : forall x_ x_ : Z, Z :=
  fun n m : Z =>
  match (n ?= m)%Z with
  | Datatypes.Eq => m
  | Datatypes.Lt => m
  | Datatypes.Gt => n
  end.

Theorem Rmult_IZR : forall z t : Z, IZR (z * t) = (IZR z * IZR t)%R.