Definition reducts_incl {A B: Type} (C: A -> B) (res1: reducts A) (res2: reducts B) : Prop :=
forall C1 rd, In (C1, rd) res1 -> In ((fun x => C(C1 x)), rd) res2.

Lemma reducts_incl_val:
forall (A: Type) a m v ty (C: expr -> A) res,
is_val a = Some(v, ty) -> reducts_incl C (step_expr RV a m) res.