proposition: Theorem round_round_minus_FTZ : forall choice1 choice2, (emin' + prec' <= emin + 1)%Z -> (2 * prec + 1 <= prec')%Z -> forall x y, FTZ_format beta emin prec x -> FTZ_format beta emin prec y -> round_round_eq (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. - now apply FTZ_exp_valid. - now apply FTZ_exp_valid. - now apply FTZ_round_round_plus_hyp. - now apply generic_format_FTZ. - now apply generic_format_FTZ. Qed.
imports: Coq(ZArith Reals Psatz) Core FTZ