(** A compilation environment (mapping) is valid in a given state if
  the registers associated with Cminor local variables and let-bound variables
  are valid in the state. *)

Definition map_valid (m: mapping) (s: state) : Prop :=
  forall r, reg_in_map m r -> reg_valid r s.

Lemma add_var_valid: forall s1 s2 map1 map2 name r i, add_var map1 name s1 = OK (r, map2) s2 i -> map_valid map1 s1 -> reg_valid r s2 /\ map_valid map2 s2.