Set Universe Polymorphism. Set Printing Universes. Inductive list {T} : Type := | cons (t : T) : list -> list. (* who needs nil anyway? *) Arguments list : clear implicits. Fixpoint map {A B} (f: A -> B) (l : list A) : list B := let '(cons t l) := l in cons (f t) (map f l). About map@{_ _}. (* Two universes, as expected. *) Definition map_Set@{} {A B : Set} := @map A B. Definition map_Prop@{} {A B : Prop} := @map A B.