proposition: Theorem generic_format_FLX_1 : generic_format beta FLX_exp 1.
proof: Proof. unfold generic_format, scaled_mantissa, cexp, F2R; simpl. rewrite Rmult_1_l, (mag_unique beta 1 1). { unfold FLX_exp. rewrite <- IZR_Zpower; [|unfold Prec_gt_0 in prec_gt_0_; lia]. rewrite Ztrunc_IZR, IZR_Zpower; [|unfold Prec_gt_0 in prec_gt_0_; lia]. rewrite <- bpow_plus. now replace (_ + _)%Z with Z0 by ring. } rewrite Rabs_R1; simpl; split; [now right|]. unfold Z.pow_pos; simpl; rewrite Zmult_1_r; apply IZR_lt. assert (H := Zle_bool_imp_le _ _ (radix_prop beta)); lia. Qed.
imports: Coq(ZArith Reals Psatz) Zaux Raux Defs Round_pred Generic_fmt Float_prop FIX Ulp Round_NE