intros x y H'.
cut (Feq x y \/ Flt x y).
intros H; case H; intros H1; auto with real.
red in |- *; apply Req_le; auto with real.
red in |- *; apply Rlt_le; auto with real.
generalize H' (Feq_bool_correct_t x y) (Flt_bool_correct_t x y).
unfold Fle_bool, Feq_bool, Flt_bool in |- *; case (Fcompare x y); auto.
Qed.

(* Specifications: *)
Theorem Fle_bool_correct_r :
forall x y : float, Fle x y -> Fle_bool x y = true.