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_incontext2_left: forall (A1 A2 B: Type) (C1: A1 -> B) res1 (C2: A2 -> B) res2, reducts_incl C1 res1 (incontext2 C1 res1 C2 res2).