more additions and corrections for the article

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / rdsx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx.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/predtysnstrong_4.ma".
-include "static_2/static/rdeq.ma".
-include "basic_2/rt_transition/lpx.ma".
-
-(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
-
-definition rdsx (h) (G) (T): predicate lenv ≝
-                             SN … (lpx h G) (rdeq T).
-
-interpretation
-   "strong normalization for unbound context-sensitive parallel rt-transition on referred entries (local environment)"
-   'PRedTySNStrong h T G L = (rdsx h G T L).
-
-(* Basic eliminators ********************************************************)
-
-(* Basic_2A1: uses: lsx_ind *)
-lemma rdsx_ind (h) (G) (T):
-               ∀Q:predicate lenv.
-               (∀L1. G ⊢ ⬈*[h,T] 𝐒⦃L1⦄ →
-                     (∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
-                     Q L1
-               ) →
-               ∀L. G ⊢ ⬈*[h,T] 𝐒⦃L⦄ →  Q L.
-#h #G #T #Q #H0 #L1 #H elim H -L1
-/5 width=1 by SN_intro/
-qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_2A1: uses: lsx_intro *)
-lemma rdsx_intro (h) (G) (T):
-                 ∀L1.
-                 (∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[T] L2 → ⊥) → G ⊢ ⬈*[h,T] 𝐒⦃L2⦄) →
-                 G ⊢ ⬈*[h,T] 𝐒⦃L1⦄.
-/5 width=1 by SN_intro/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-(* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
-lemma rdsx_fwd_pair_sn (h) (G):
-                       ∀I,L,V,T. G ⊢ ⬈*[h,②{I}V.T] 𝐒⦃L⦄ →
-                       G ⊢ ⬈*[h,V] 𝐒⦃L⦄.
-#h #G #I #L #V #T #H
-@(rdsx_ind … H) -L #L1 #_ #IHL1
-@rdsx_intro #L2 #HL12 #HnL12
-/4 width=3 by rdeq_fwd_pair_sn/
-qed-.
-
-(* Basic_2A1: uses: lsx_fwd_flat_dx *)
-lemma rdsx_fwd_flat_dx (h) (G):
-                       ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄ →
-                       G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
-#h #G #I #L #V #T #H 
-@(rdsx_ind … H) -L #L1 #_ #IHL1
-@rdsx_intro #L2 #HL12 #HnL12
-/4 width=3 by rdeq_fwd_flat_dx/
-qed-.
-
-fact rdsx_fwd_pair_aux (h) (G):
-     ∀L. G ⊢ ⬈*[h,#0] 𝐒⦃L⦄ →
-     ∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
-#h #G #L #H
-@(rdsx_ind … H) -L #L1 #_ #IH #I #K1 #V #H destruct
-/5 width=5 by lpx_pair, rdsx_intro, rdeq_fwd_zero_pair/
-qed-.
-
-lemma rdsx_fwd_pair (h) (G):
-                    ∀I,K,V. G ⊢ ⬈*[h,#0] 𝐒⦃K.ⓑ{I}V⦄ → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
-/2 width=4 by rdsx_fwd_pair_aux/ qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-(* Basic_2A1: uses: lsx_inv_flat *)
-lemma rdsx_inv_flat (h) (G):
-      ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄ →
-      ∧∧ G ⊢ ⬈*[h,V] 𝐒⦃L⦄ & G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
-/3 width=3 by rdsx_fwd_pair_sn, rdsx_fwd_flat_dx, conj/ qed-.
-
-(* Basic_2A1: removed theorems 9:
-              lsx_ge_up lsx_ge
-              lsxa_ind lsxa_intro lsxa_lleq_trans lsxa_lpxs_trans lsxa_intro_lpx lsx_lsxa lsxa_inv_lsx
-*)