End Fprop_relative_FLT.

(* Specifications: *)
Lemma error_N_FLT :
forall (emin prec : Z), (0 < prec)%Z ->
forall (choice : Z -> bool),
forall (x : R),
exists eps eta : R,
(Rabs eps <= /2 * bpow (-prec + 1))%R /\
(Rabs eta <= /2 * bpow emin)%R /\
(eps * eta = 0)%R /\
(round beta (FLT_exp emin prec) (Znearest choice) x
= x * (1 + eps) + eta)%R.
Lemma error_N_FLT :
forall (emin prec : Z), (0 < prec)%Z ->
forall (choice : Z -> bool),
forall (x : R),
exists eps eta : R,
(Rabs eps <= /2 * bpow (-prec + 1))%R /\
(Rabs eta <= /2 * bpow emin)%R /\
(eps * eta = 0)%R /\
(round beta (FLT_exp emin prec) (Znearest choice) x
= x * (1 + eps) + eta)%R.