+ NCic.inductiveFun list * NCic.f_attr * int
+
+(* invalidate the object and all those that entered the environment after it *)
+val invalidate_item:
+ [ `Obj of NUri.uri * NCic.obj
+ | `Constr of NCic.universe * NCic.universe ] -> unit
+
+val invalidate: unit -> unit
+
+val set_typecheck_obj: (NCic.obj -> unit) -> unit
+
+(* =========== universes ============= *)
+
+(* utils *)
+val ppsort : Format.formatter -> NCic.sort -> unit
+val pp_constraints: unit -> string
+val get_universes: unit -> NCic.universe list
+
+(* The type of Prop, smaller than any other type *)
+val type0: NCic.universe
+
+(* use to type products *)
+val max: NCic.universe -> NCic.universe -> NCic.universe
+
+(* raise BadConstraints if the second arg. is an inferred universe or
+ * if the added constraint gives circularity *)
+exception BadConstraint of string Lazy.t;;
+val add_lt_constraint: NCic.universe -> NCic.universe -> unit
+val universe_eq: NCic.universe -> NCic.universe -> bool
+val universe_leq: NCic.universe -> NCic.universe -> bool
+
+(* checks if s1 <= s2 *)
+val are_sorts_convertible: test_eq_only:bool -> NCic.sort -> NCic.sort -> bool
+
+(* to type a Match *)
+val allowed_sort_elimination: NCic.sort -> NCic.sort -> [ `Yes | `UnitOnly ]
+
+(* algebraic successor function *)
+exception UntypableSort of string Lazy.t
+exception AssertFailure of string Lazy.t
+val typeof_sort: NCic.sort -> NCic.sort
+
+(* looks for a declared universe that is the least one above the input *)
+val sup : NCic.universe -> NCic.universe option