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+From HoTT Require Import Colimits.Quotient.
+
+(** This eases with reading the checks. *)
+Set Printing Universes.
+Unset Printing Notations.
+
+(** Enforcing universe constraints on Quotient types *)
+
+(** Quotient types have 3 universe variables:
+  - The type to be quotiented, [A]
+  - The equivalence relation, [R]
+  - The universe the quotient type lives in, think of as a max of the other 2 *)
+Check Quotient@{i j k}.
+Check class_of@{i j k}.
+Check qglue@{i j k}.
+
+(** TODO: these are less general than it should be. *)
+Check Quotient_ind_hprop@{i j k}.
+Check in_class@{i j k r}.
+Check decidable_in_class@{u1 u2 u3 u4 u5}.
+Check path_in_class_of@{i j k r _}.
+Check related_quotient_paths@{i j k r}.
+
+(** Universe levels of the quotient + the target type. *)
+Check Quotient_ind@{i j k r}.
+Check Quotient_rec@{i j k r}.
+Check Quotient_ind_beta_qglue@{i j k r}.
+Check Quotient_rec_beta_qglue@{i j k r}.