intros x y H'.
case (Rtotal_order (FtoRradix y) (FtoRradix x)); auto with real.
intros H'0; red in |- *; apply Rlt_le; auto with real.
intros H'0; elim H'0; clear H'0; intros H'1.
red in |- *; rewrite H'1; auto with real.
Contradict H'; rewrite Flt_bool_correct_r; auto with real.
red in |- *; intros H'; discriminate.
Qed.
Definition Fle_bool (x y : float) :=
match Fcompare x y with
| Lt => true
| Eq => true
| _ => false
end.

Theorem Fle_bool_correct_t :
forall x y : float, Fle_bool x y = true -> Fle x y.