intros p q H' H'0 H'1 H'2; Casec H'2; intros H'2.
apply Zlt_le_weak.
apply FweightLt; auto.
rewrite (FweightEq p q); auto with zarith.
Qed.

Theorem FinductPosAux :
forall (P : float -> Prop) (p : float),
(0 <= p)%R ->
Fcanonic radix b p ->
P p ->
(forall q : float,
Fcanonic radix b q -> (p <= q)%R -> P q -> P (FSucc b radix precision q)) ->
forall x : Z,
(0 <= x)%Z ->
forall q : float,
x = (Fweight q - Fweight p)%Z -> Fcanonic radix b q -> (p <= q)%R -> P q.