proposition: Theorem round_round_div_FTZ : forall choice1 choice2, (exists n, (beta = 2 * n :> Z)%Z) -> (emin' + prec' <= emin - 1)%Z -> (2 * prec <= prec')%Z -> forall x y, y <> 0 -> 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 Ebeta Hemin Hprec x y Nzy Fx Fy. apply round_round_div. - now apply FTZ_exp_valid. - now apply FTZ_exp_valid. - exact Ebeta. - now apply FTZ_round_round_div_hyp. - exact Nzy. - now apply generic_format_FTZ. - now apply generic_format_FTZ. Qed.
imports: Coq(ZArith Reals Psatz) Core FTZ