Definition Fcanonic (a : float) := Fnormal a \/ Fsubnormal a.

Theorem FnormalLtPos : forall p q : float, Fnormal p -> Fnormal q -> (0 <= p)%R -> (p < q)%R -> (Fexp p < Fexp q)%Z \/ Fexp p = Fexp q /\ (Fnum p < Fnum q)%Z.