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

Lemma FLX_double_round_plus_hyp : (2 * prec + 1 <= prec')%Z -> double_round_plus_hyp (FLX_exp prec) (FLX_exp prec').