proposition: Theorem fix_float_of_fix : forall rdir {Hrnd : Valid_rnd rdir} p d xn zn x, FIX x xn -> Zle_bool zn xn = true -> FIX (rounding_float rdir p d x) zn.
proof: Proof. Proof with auto with typeclass_instances. intros rdir Hrnd p d xn zn x Hx Hb. generalize (Zle_bool_imp_le _ _ Hb). clear Hb. intro H1. apply FIX_iff_generic. apply generic_round_generic... apply FIX_iff_generic. now apply fix_le with xn. Qed.
imports: Coq(Bool ZArith Reals Lia) Flocq(Core Digits Round Relative) Gappa_definitions Gappa_dyadic Gappa_pred_bnd Gappa_round_def Gappa_round_aux Gappa_round