diff --git a/TODO.md b/TODO.md
index aa496b5f..0fe90bb2 100644
--- a/TODO.md
+++ b/TODO.md
@@ -1,8 +1,6 @@
 TODO
 ----
 
-- create a pos file for each part
-
 - get rid of use file? in pos files, set pos to -1 for unused theorems
 
 - proofs can be simplified in parallel by working on the proof of each named theorem separately
diff --git a/main.ml b/main.ml
index 83aec8fe..395f739d 100644
--- a/main.ml
+++ b/main.ml
@@ -517,7 +517,8 @@ and command = function
      iter_proofs_at simp;
      close_in !Xproof.ic_prf;
      close_out oc;
-     log "%d simplifications (%d%%)\n" !n (percent !n (nb_proofs()));
+     let nb_proofs = Array.length !prf_pos in
+     log "%d simplifications (%d%%)\n" !n (percent !n nb_proofs);
      (* replace file.prf by file-simp.prf, and recompute file.pos and
         file.use *)
      log "replace %s.prf by %s-simp.prf ...\n" b b;
@@ -535,7 +536,7 @@ and command = function
      read_pos b;
      init_proof_reading b;
      let map_thid_name = read_thm b in
-     let nb_proofs = nb_proofs() in
+     let nb_proofs = Array.length !prf_pos in
      let useful = Array.make nb_proofs false in
      let rec mark_as_useful = function
        | [] -> ()
@@ -701,26 +702,25 @@ and command = function
      let ic = open_in_bin dump_file in
      let nb_parts = input_value ic in
 
-     let k = integer k and x = integer x and y = integer y
-     and nb_proofs = nb_proofs() in
+     let k = integer k and x = integer x and y = integer y in
      if k < 1 || k > nb_parts || x < 0 || y < x then wrong_arg();
      read_sig b;
+     let suffix = "_part_" ^ string_of_int k in
      read_pos b;
      init_proof_reading b;
-     cur_part_max := (k * nb_proofs) / nb_parts;
      read_use b;
      if is_dk f then
        begin
          Xdk.export_proofs_part b k x y;
-         let suffix = "_part_" ^ string_of_int k in
          Xdk.export_term_abbrevs b suffix;
          Xdk.export_type_abbrevs b suffix
        end
      else
        begin
+         (* used in xlp to know whether a theorem can be declared as private *)
+         cur_part_max := y;
          let dg = input_value ic in
          Xlp.export_proofs_part b dg k x y;
-         let suffix = "_part_" ^ string_of_int k in
          Xlp.export_term_abbrevs b suffix;
          Xlp.export_type_abbrevs b suffix
        end;
@@ -729,10 +729,12 @@ and command = function
      0
 
   | ["prf";x;y;b] ->
-     let x = integer x and y = integer y and n = nb_proofs() in
-     if x < 0 || y < 0 || x > y || x >= n || y >= n then wrong_arg();
      read_sig b;
      read_pos b;
+     let x = integer x and y = integer y
+         and nb_proofs = Array.length !prf_pos in
+     if x < 0 || y < 0 || x > y || x >= nb_proofs || y >= nb_proofs then
+       wrong_arg();
      init_proof_reading b;
      read_use b;
      Xlp.export_one_file_by_prf b x y;
@@ -743,8 +745,9 @@ and command = function
      let nb_parts = integer nb_parts in
      if nb_parts < 1 then wrong_arg();
      read_pos b;
+     let nb_proofs = Array.length !prf_pos in
      init_proof_reading b;
-     Xlp.gen_lp_makefile_one_file_by_prf b (nb_proofs()) nb_parts;
+     Xlp.gen_lp_makefile_one_file_by_prf b nb_proofs nb_parts;
      close_in !Xproof.ic_prf;
      0
 
@@ -752,8 +755,9 @@ and command = function
      let nb_parts = integer nb_parts in
      if nb_parts < 1 then wrong_arg();
      read_pos b;
+     let nb_proofs = Array.length !prf_pos in
      init_proof_reading b;
-     Xlp.gen_coq_makefile_one_file_by_prf b (nb_proofs()) nb_parts;
+     Xlp.gen_coq_makefile_one_file_by_prf b nb_proofs nb_parts;
      close_in !Xproof.ic_prf;
      0
 
diff --git a/xdk.ml b/xdk.ml
index c375df13..c2601b48 100644
--- a/xdk.ml
+++ b/xdk.ml
@@ -792,8 +792,7 @@ let export_theorems_as_axioms b map_thid_name =
 
 let export_proofs_part b k x y =
   part := Some k;
-  export b ("_part_" ^ string_of_int k)
-    (fun oc -> proofs_in_range oc (Inter(x,y)))
+  export b ("_part_" ^ string_of_int k) (fun oc -> proofs_in_interval oc x y)
 ;;
 
 (****************************************************************************)
diff --git a/xlib.ml b/xlib.ml
index e56d6d26..f1bbb4c3 100644
--- a/xlib.ml
+++ b/xlib.ml
@@ -493,8 +493,7 @@ let deps (Proof(_,content)) =
 ;;
 
 (* [count_thm_uses a p] increments by 1 every [a.(i)] such that [i] is
-   a dependence of [p]. [a] must be an array of integers of size
-   [nb_proofs()]. *)
+   a dependence of [p]. *)
 let count_thm_uses (a : int array) (p : proof) : unit =
   List.iter (fun k -> Array.set a k (Array.get a k + 1)) (deps p)
 ;;
diff --git a/xproof.ml b/xproof.ml
index 36e972bb..3971cc8b 100644
--- a/xproof.ml
+++ b/xproof.ml
@@ -25,9 +25,6 @@ let read_pos basename =
   prf_pos := input_value ic;
   close_in ic
 
-(* Can be used after [read_pos] only. *)
-let nb_proofs() = Array.length !prf_pos;;
-
 let ic_prf : in_channel ref = ref stdin;;
 
 let init_proof_reading basename =
@@ -53,13 +50,14 @@ let read_use basename = last_use := read_val (basename ^ ".use");;
 let cur_part_max : int ref = ref (-1);;
 
 (* [iter_proofs_at f] runs [f k (proof_at k)] on all proof index [k]
-   from 0 to [nb_proofs() - 1] (including unused proofs). Can be used
-   after [read_pos] and [init_proof_reading] only. *)
+   from 0 to [nb_proofs - 1] (including unused proofs), where
+   [nb_proofs = Array.length !prf_pos]. Can be used after [read_pos]
+   and [init_proof_reading] only. *)
 let iter_proofs_at (f : int -> proof -> unit) =
   let idx = ref 0 in
-  let n = nb_proofs() in
+  let nb_proofs = Array.length !prf_pos in
   try
-    while !idx < n do
+    while !idx < nb_proofs do
       let k = !idx in
       f k (proof_at k);
       idx := k + 1