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diff --git a/library/univops.ml b/library/univops.ml
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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+open Term
+open Univ
+open Declarations
+
+let universes_of_constr c =
+  let rec aux s c = 
+    match kind_of_term c with
+    | Const (_, u) | Ind (_, u) | Construct (_, u) ->
+      LSet.fold LSet.add (Instance.levels u) s
+    | Sort u when not (Sorts.is_small u) -> 
+      let u = univ_of_sort u in
+      LSet.fold LSet.add (Universe.levels u) s
+    | _ -> fold_constr aux s c
+  in aux LSet.empty c
+
+let universes_of_inductive mind =
+  let process auctx =
+    let u = Univ.AUContext.instance auctx in
+    let univ_of_one_ind oind = 
+      let arity_univs =
+        Context.Rel.fold_outside
+          (fun decl unvs ->
+             Univ.LSet.union
+              (Context.Rel.Declaration.fold_constr
+                 (fun cnstr unvs ->
+                    let cnstr = Vars.subst_instance_constr u cnstr in
+                    Univ.LSet.union
+                      (universes_of_constr cnstr) unvs)
+              decl Univ.LSet.empty) unvs)
+        oind.mind_arity_ctxt ~init:Univ.LSet.empty
+      in
+      Array.fold_left (fun unvs cns ->
+          let cns = Vars.subst_instance_constr u cns in
+          Univ.LSet.union (universes_of_constr cns) unvs) arity_univs 
+       oind.mind_nf_lc
+    in
+    let univs = 
+      Array.fold_left
+        (fun unvs pk ->
+           Univ.LSet.union
+             (univ_of_one_ind pk) unvs
+        )
+        Univ.LSet.empty mind.mind_packets 
+    in
+    let mindcnt =  Univ.UContext.constraints (Univ.instantiate_univ_context auctx) in
+    let univs = Univ.LSet.union univs (Univ.universes_of_constraints mindcnt) in
+    univs
+  in
+  match mind.mind_universes with
+  | Monomorphic_ind _ -> LSet.empty
+  | Polymorphic_ind auctx -> process auctx
+  | Cumulative_ind cumi -> process (Univ.ACumulativityInfo.univ_context cumi)
+
+let restrict_universe_context (univs,csts) s =
+  (* Universes that are not necessary to typecheck the term.
+     E.g. univs introduced by tactics and not used in the proof term. *)
+  let diff = LSet.diff univs s in
+  let rec aux diff candid univs ness = 
+    let (diff', candid', univs', ness') = 
+      Constraint.fold
+	(fun (l, d, r as c) (diff, candid, univs, csts) ->
+	  if not (LSet.mem l diff) then
+	    (LSet.remove r diff, candid, univs, Constraint.add c csts)
+	  else if not (LSet.mem r diff) then
+	    (LSet.remove l diff, candid, univs, Constraint.add c csts)
+	  else (diff, Constraint.add c candid, univs, csts))
+	candid (diff, Constraint.empty, univs, ness)
+    in
+      if ness' == ness then (LSet.diff univs diff', ness)
+      else aux diff' candid' univs' ness'
+  in aux diff csts univs Constraint.empty