Qed.
Coercion IZR : Z >-> R.
Coercion INR : nat >-> R.
Coercion Z_of_nat : nat >-> Z.
Definition FtoR (x : float) := (Fnum x * powerRZ (IZR radix) (Fexp x))%R.
Local Coercion FtoR : float >-> R.

Theorem FzeroisReallyZero : forall z : Z, Fzero z = 0%R :>R.
intros z; unfold FtoR in |- *; simpl in |- *; auto with real.