Definition irrelevant G D (a : tm) :=
(forall x A, binds x (Tm A) G -> x `notin` fv_tm (erase a)) /\ AnnGood G D.

(* Other statement? Lemma progress : forall a A G D, AnnGood G D -> AnnTyping G a A -> CoercedValue a \/ exists a', head_reduction G a a'. *)
Lemma progress : forall G a A, irrelevant G (dom G) a -> AnnTyping G a A -> CoercedValue a \/ exists a', head_reduction G a a'.
Inductive multi (rel : tm -> tm -> Prop) : tm -> tm -> Prop :=
| multi_refl : forall a, lc_tm a -> multi rel a a
| multi_step : forall a b c, rel a b -> multi rel b c -> multi rel a c.