update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cnh.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh.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/notation/relations/preditnormal_4.ma".
+include "static_2/syntax/theq.ma".
+include "basic_2/rt_transition/cpm.ma".
+
+(* NORMAL TERMS FOR HEAD T-UNUNBOUND RT-TRANSITION **************************)
+
+definition cnh (h) (G) (L): predicate term ≝
+           λT1. ∀n,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → T1 ⩳ T2.
+
+interpretation
+   "normality for head t-unbound context-sensitive parallel rt-transition (term)"
+   'PRedITNormal h G L T = (cnh h G L T).
+
+(* Basic properties *********************************************************)
+
+lemma cnh_sort (h) (G) (L): ∀s. ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃⋆s⦄.
+#h #G #L #s1 #n #X #H
+elim (cpm_inv_sort1 … H) -H #H #_ destruct //
+qed.
+
+lemma cnh_ctop (h) (G): ∀i. ⦃G,⋆⦄ ⊢ ⥲[h] 𝐍⦃#i⦄.
+#h #G * [| #i ] #n #X #H
+[ elim (cpm_inv_zero1 … H) -H *
+  [ #H #_ destruct //
+  | #Y #X1 #X2 #_ #_ #H destruct
+  | #m #Y #X1 #X2 #_ #_ #H destruct
+  ]
+| elim (cpm_inv_lref1 … H) -H *
+  [ #H #_ destruct //
+  | #Z #Y #X0 #_ #_ #H destruct
+  ]
+]
+qed.
+
+lemma cnh_zero (h) (G) (L): ∀I. ⦃G,L.ⓤ{I}⦄ ⊢ ⥲[h] 𝐍⦃#0⦄.
+#h #G #L #I #n #X #H 
+elim (cpm_inv_zero1 … H) -H *
+[ #H #_ destruct //
+| #Y #X1 #X2 #_ #_ #H destruct
+| #m #Y #X1 #X2 #_ #_ #H destruct
+]
+qed.
+
+lemma cnh_gref (h) (G) (L): ∀l. ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃§l⦄.
+#h #G #L #l1 #n #X #H
+elim (cpm_inv_gref1 … H) -H #H #_ destruct //
+qed.
+
+lemma cnh_abst (h) (p) (G) (L): ∀W,T. ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃ⓛ{p}W.T⦄.
+#h #p #G #L #W1 #T1 #n #X #H
+elim (cpm_inv_abst1 … H) -H #W2 #T2 #_ #_ #H destruct
+/1 width=1 by theq_pair/
+qed.
+
+lemma cnh_abbr_neg (h) (G) (L): ∀V,T. ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃-ⓓV.T⦄.
+#h #G #L #V1 #T1 #n #X #H
+elim (cpm_inv_abbr1 … H) -H *
+[ #W2 #T2 #_ #_ #H destruct /1 width=1 by theq_pair/
+| #X1 #_ #_ #H destruct
+]
+qed.