intros p H'.
apply FcanonicUnique; auto.
apply FnormalizeCanonic; auto.
apply FcanonicBound with (1 := H'); auto.
apply FnormalizeCorrect; auto.
Qed.

Theorem FcanonicPosFexpRlt :
forall x y : float,
(0 <= x)%R ->
(0 <= y)%R -> Fcanonic x -> Fcanonic y -> (Fexp x < Fexp y)%Z -> (x < y)%R.