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diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/item_sh.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/item_sh.ma
deleted file mode 100644
index 9e0b03f73..000000000
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/item_sh.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "ground_2/lib/arith.ma".
-
-(* SORT HIERARCHY ***********************************************************)
-
-(* sort hierarchy specification *)
-record sh: Type[0] ≝ {
-   next   : nat → nat;     (* next sort in the hierarchy *)
-   next_lt: ∀s. s < next s (* strict monotonicity condition *)
-}.
-
-definition sh_N: sh ≝ mk_sh S ….
-// defined.
-
-(* Basic properties *********************************************************)
-
-lemma nexts_le: ∀h,s,n. s ≤ (next h)^n s.
-#h #s #n elim n -n // normalize #n #IH
-lapply (next_lt h ((next h)^n s)) #H
-lapply (le_to_lt_to_lt … IH H) -IH -H /2 width=2 by lt_to_le/
-qed.
-
-lemma nexts_lt: ∀h,s,n. s < (next h)^(↑n) s.
-#h #s #n normalize
-lapply (nexts_le h s n) #H
-@(le_to_lt_to_lt … H) //
-qed.
-
-axiom nexts_dec: ∀h,s1,s2. Decidable (∃n. (next h)^n s1 = s2).
-
-axiom nexts_inj: ∀h,s,n1,n2. (next h)^n1 s = (next h)^n2 s → n1 = n2.