proposition: Lemma round_round_mult_beta_odd_aux2 : forall (fexp1 fexp2 : Z -> Z), Valid_exp fexp1 -> Valid_exp fexp2 -> forall (choice1 choice2 : Z -> bool), (forall ex, (fexp2 ex <= fexp1 ex)%Z) -> forall x y, 0 <= x -> 0 <= y -> generic_format beta fexp1 x -> generic_format beta fexp1 y -> round_round_eq beta fexp1 fexp2 choice1 choice2 (x * y).
proof: Proof. intros fexp1 fexp2 Vfexp1 Vfexp2 choice1 choice2 Hfexp x y Nnx Nny Fx Fy. destruct (Req_dec x 0) as [Zx|Nzx]. - unfold round_round_eq. now rewrite Zx, Rmult_0_l, round_0; [|apply valid_rnd_N]. - assert (Px : 0 < x); [lra|]. destruct (Req_dec y 0) as [Zy|Nzy]. + unfold round_round_eq. now rewrite Zy, Rmult_0_r, round_0; [|apply valid_rnd_N]. + assert (Py : 0 < y); [lra|]. now apply round_round_mult_beta_odd_aux1. Qed.
imports: Coq(ZArith Reals Psatz) Flocq(Core FTZ Double_rounding)