Definition FNodd (p : float) := Fodd (Fnormalize radix b precision p).Definition FNeven (p : float) := Feven (Fnormalize radix b precision p).

(* Specifications: *)
Theorem FNoddEq : forall f1 f2 : float, Fbounded b f1 -> Fbounded b f2 -> f1 = f2 :>R -> FNodd f1 -> FNodd f2.
Theorem FNevenEq : forall f1 f2 : float, Fbounded b f1 -> Fbounded b f2 -> f1 = f2 :>R -> FNeven f1 -> FNeven f2.
Theorem FNevenFop : forall p : float, FNeven p -> FNeven (Fopp p).
Theorem FNoddFop : forall p : float, FNodd p -> FNodd (Fopp p).
Theorem FNoddSuc : forall p : float, Fbounded b p -> FNodd p -> FNeven (FNSucc b radix precision p).
Theorem FNevenSuc : forall p : float, Fbounded b p -> FNeven p -> FNodd (FNSucc b radix precision p).
Theorem FNevenPred : forall p : float, Fbounded b p -> FNodd p -> FNeven (FNPred b radix precision p).
Theorem FNoddPred : forall p : float, Fbounded b p -> FNeven p -> FNodd (FNPred b radix precision p).
Theorem FNevenOrFNodd : forall p : float, FNeven p \/ FNodd p.
Theorem FnOddNEven : forall n : float, FNodd n -> ~ FNeven n.
Theorem FEvenD : forall p : float, Fbounded b p -> Feven p -> exists q : float, Fbounded b q /\ p = (2%nat * q)%R :>R.
Theorem FNEvenD : forall p : float, Fbounded b p -> FNeven p -> exists q : float, Fbounded b q /\ p = (2%nat * q)%R :>R.