intros x y H'.
cut (0 < y - x)%R; auto with arith.
2: apply Rplus_lt_reg_l with (r := FtoRradix x); rewrite Rplus_0_r;
rewrite Rplus_minus; auto with real.
intros H'0.
cut (Fdiff x y < 0)%R; auto with arith.
intros H'1.
cut (Fdiff x y < 0)%Z; auto with zarith.
intros H'2; generalize (Zlt_compare _ _ H'2);
unfold Flt_bool, Fcompare, Zcompare in |- *; case (Fdiff x y);
auto with arith; intros; contradiction.
apply lt_IZR; auto with arith.
apply (Rlt_monotony_contra_exp radix) with (z := Zmin (Fexp x) (Fexp y));
auto with arith real; rewrite Rmult_0_l.
rewrite Fdiff_correct; auto with real.
Qed.

Theorem Flt_bool_correct_f :
forall x y : float, Flt_bool x y = false -> Fle y x.