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diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/twhnf.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/twhnf.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 "basic_2/grammar/tshf.ma".
-include "basic_2/reducibility/tpr.ma".
-
-(* CONTEXT-FREE WEAK HEAD NORMAL TERMS **************************************)
-
-definition twhnf: predicate term ≝ NF … tpr tshf.
-
-interpretation
-   "context-free weak head normality (term)"
-   'WHdNormal T = (twhnf T).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma twhnf_inv_tshf: ∀T. 𝐖𝐇𝐍⦃T⦄ → T ≈ T.
-normalize /2 width=1/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma tpr_tshf: ∀T1,T2. T1 ➡ T2 → T1 ≈ T1 → T1 ≈ T2.
-#T1 #T2 #H elim H -T1 -T2 //
-[ #I #V1 #V2 #T1 #T2 #_ #_ #_ #IHT12 #H
-  elim (tshf_inv_flat1 … H) -H #W2 #U2 #HT1U2 #HT1 #_ #H1 #H2 destruct
-  lapply (IHT12 HT1U2) -IHT12 -HT1U2 #HUT2
-  lapply (simple_tshf_repl_dx … HUT2 HT1) /2 width=1/
-| #a #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #H
-  elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #H
-  elim (simple_inv_bind … H)
-| #a #I #V1 #V2 #T1 #T #T2 #_ #_ #_ #_ #_ #H
-  elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct //
-| #a #V2 #V1 #V #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
-  elim (tshf_inv_flat1 … H) -H #U1 #U2 #_ #H
-  elim (simple_inv_bind … H)
-| #V #T #T1 #T2 #_ #_ #_ #H
-  elim (tshf_inv_bind1 … H) -H #W2 #U2 #H1 * #H2 destruct
-| #V #T1 #T2 #_ #_ #H
-  elim (tshf_inv_flat1 … H) -H #W2 #U2 #_ #_ #_ #H destruct
-]
-qed.
-
-lemma twhnf_tshf: ∀T. T ≈ T → 𝐖𝐇𝐍⦃T⦄.
-/3 width=1/ qed.