Definition reg: Type := positive.Definition eq := peq.Definition typenv := PMap.t typ.(** Mappings from registers to some type. *)

Module Regmap := PMap.Definition regmap_optget
    (A: Type) (or: option reg) (dfl: A) (rs: Regmap.t A) : A :=
  match or with
  | None => dfl
  | Some r => Regmap.get r rs
  end.Definition regmap_optset
    (A: Type) (or: option reg) (v: A) (rs: Regmap.t A) : Regmap.t A :=
  match or with
  | None => rs
  | Some r => Regmap.set r v rs
  end.Definition regmap_setres
    (A: Type) (res: builtin_res reg) (v: A) (rs: Regmap.t A) : Regmap.t A :=
  match res with
  | BR r => Regmap.set r v rs
  | _ => rs
  end.Notation "a # b" := (Regmap.get b a) (at level 1) : rtl.Notation "a ## b" := (List.map (fun r => Regmap.get r a) b) (at level 1) : rtl.Notation "a # b <- c" := (Regmap.set b c a) (at level 1, b at next level) : rtl.

Lemma set_res_lessdef: forall res v1 v2 rs1 rs2, Val.lessdef v1 v2 -> regs_lessdef rs1 rs2 -> regs_lessdef (regmap_setres res v1 rs1) (regmap_setres res v2 rs2).