intros p q H' H'0 H'1.
apply (FdigitEq radix); auto.
apply FnormalNotZero; auto.
apply trans_equal with (y := precision); auto with float.
apply sym_equal; auto with float.
Qed.

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.