-(**************************************************************************)
-(* ___ *)
-(* ||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 thnf: predicate term ≝ NF … tpr tshf.
-
-interpretation
- "context-free head normality (term)"
- 'HdNormal T = (thnf T).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma thnf_inv_tshf: ∀T. 𝐇𝐍⦃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 thnf_tshf: ∀T. T ≈ T → 𝐇𝐍⦃T⦄.
-/3 width=1/ qed.