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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                  *)
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notation "hvbox( L ⊢ break 𝐇𝐍 ⦃ term 46 T ⦄ )"
   non associative with precedence 45
   for @{ 'HdNormal $L $T }.

include "basic_2/reduction/cpr_tshf.ma".

(* CONTEXT-SENSITIVE WEAK HEAD NORMAL TERMS *********************************)

definition chnf: lenv → predicate term ≝ λL. NF … (cpr L) tshf.

interpretation
   "context-sensitive head normality (term)"
   'HdNormal L T = (chnf L T).

(* Basic inversion lemmas ***************************************************)

lemma chnf_inv_tshf: ∀L,T. L ⊢ 𝐇𝐍⦃T⦄ → T ≈ T.
normalize /2 width=1/
qed-.

(* Basic properties *********************************************************)

lemma tshf_thnf: ∀T. T ≈ T → ⋆ ⊢ 𝐇𝐍⦃T⦄.
#T #HT #T2 #H elim (cpr_fwd_tshf1 … H) -H //
#H elim H //
qed.