proposition: Theorem round_round_mult_FLX : (2 * prec <= prec')%Z -> forall x y, FLX_format beta prec x -> FLX_format beta prec y -> round beta (FLX_exp prec) rnd (round beta (FLX_exp prec') rnd (x * y)) = round beta (FLX_exp prec) rnd (x * y).
proof: Proof. intros Hprec x y Fx Fy. apply round_round_mult; [|now apply generic_format_FLX|now apply generic_format_FLX]. unfold round_round_mult_hyp; split; intros ex ey; unfold FLX_exp; lia. Qed.
imports: Coq(ZArith Reals Psatz) Core FTZ