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 Rle_Rinv : forall x y : R, (0 < x)%R -> (x <= y)%R -> (/ y <= / x)%R.