Set Universe Polymorphism. Notation Type1 := $(let U := constr:(Type) in let gt := constr:(Set : U) in exact U)$ (only parsing). Inductive Empty : Type1 := . Fail Check Empty : Set. (* Toplevel input, characters 15-116: Error: Conversion test raised an anomaly *) (* Now we make sure it's not an anomaly *) Goal True. Proof. try exact (let x := Empty : Set in I). exact I. Defined.