Scheme context_ind2 := Minimality for context Sort Prop
  with contextlist_ind2 := Minimality for contextlist Sort Prop.Combined Scheme context_contextlist_ind from context_ind2, contextlist_ind2.

Lemma context_compose: forall k2 k3 C2, context k2 k3 C2 -> forall k1 C1, context k1 k2 C1 -> context k1 k3 (fun x => C2(C1 x)) with contextlist_compose: forall k2 C2, contextlist k2 C2 -> forall k1 C1, context k1 k2 C1 -> contextlist k1 (fun x => C2(C1 x)).