Definition double_round_plus_beta_ge_3_hyp fexp1 fexp2 :=
  (forall ex ey, (fexp1 (ex + 1) <= ey)%Z -> (fexp2 ex <= fexp1 ey)%Z)
  /\ (forall ex ey, (fexp1 (ex - 1) + 1 <= ey)%Z -> (fexp2 ex <= fexp1 ey)%Z)
  /\ (forall ex ey, (fexp1 ex <= ey)%Z -> (fexp2 ex <= fexp1 ey)%Z)
  /\ (forall ex ey, (ex - 1 <= ey)%Z -> (fexp2 ex <= fexp1 ey)%Z).

Lemma FTZ_double_round_plus_beta_ge_3_hyp : (emin' + prec' <= emin + 1)%Z -> (2 * prec <= prec')%Z -> double_round_plus_beta_ge_3_hyp (FTZ_exp emin prec) (FTZ_exp emin' prec').