update in static_2 and 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
deleted file mode 100644 (file)
index 9e549a9..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh.ma
+++ /dev/null
@@ -1,75 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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.