Module Short. Set Universe Polymorphism. Inductive relevant (A : Type) (B : Type) : Prop := . Section foo. Variables A B : Type. Definition foo := prod (relevant A B) A. End foo. Section bar. Variable A : Type. Variable B : Type. Definition bar := prod (relevant A B) A. End bar. Set Printing Universes. Check bar nat Set : Set. (* success *) Check foo nat Set : Set. (* Toplevel input, characters 6-17: Error: The term "foo (* Top.303 Top.304 *) nat Set" has type "Type (* Top.304 *)" while it is expected to have type "Set" (Universe inconsistency: Cannot enforce Top.304 = Set because Set < Top.304)). *) End Short.