Section MonoidalCategoryLaws.
Context {E : Type -> Type}.
Local Open Scope cat.
Fact lift_case_sum {A B C} (ac : A -> C) (bc : B -> C) :
case_ (lift_ktree_ E _ _ ac) (lift_ktree bc)
⩯ lift_ktree (case__ Fun ac bc).
(** *** [Unitors] lemmas *)
(* This is probably generalizable into [Basics.Category]. *)

Lemma unit_r_ktree (A : Type) :
unit_r ⩯ lift_ktree_ E (A + void) _ unit_r.