proposition: Theorem round_round_minus_beta_odd_FTZ : forall choice1 choice2, (emin' + prec' <= emin + prec)%Z -> (prec <= prec')%Z -> forall x y, FTZ_format beta emin prec x -> FTZ_format beta emin prec y -> round_round_eq beta (FTZ_exp emin prec) (FTZ_exp emin' prec') choice1 choice2 (x - y).
proof: Proof. intros choice1 choice2 Hemin Hprec x y Fx Fy. apply round_round_minus_beta_odd. - now apply FTZ_exp_valid. - now apply FTZ_exp_valid. - intro ex; unfold FTZ_exp. unfold Prec_gt_0 in prec_gt_0_. destruct (Z.ltb_spec (ex - prec') emin'); destruct (Z.ltb_spec (ex - prec) emin); lia. - now apply generic_format_FTZ. - now apply generic_format_FTZ. Qed.
imports: Coq(ZArith Reals Psatz) Flocq(Core FTZ Double_rounding)