Definition Rbar_div (x y : Rbar) : Rbar :=
Rbar_mult x (Rbar_inv y).
Arguments Rbar_div !x !y /.
Definition is_Rbar_div (x y z : Rbar) : Prop :=
is_Rbar_mult x (Rbar_inv y) z.
Definition ex_Rbar_div (x y : Rbar) : Prop :=
ex_Rbar_mult x (Rbar_inv y).
Arguments ex_Rbar_div !x !y /.
Definition Rbar_div_pos (x : Rbar) (y : posreal) :=
match x with
| Finite x => Finite (x/y)
| _ => x
end.
(** * Compatibility with real numbers *)
(** For equality and order. The compatibility of addition and multiplication is proved in Rbar_seq *)

Lemma Rbar_finite_neq (x y : R) :
Finite x <> Finite y <-> x <> y.