refactoring to park the notions:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsx_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma
deleted file mode 100644 (file)
index 07f3d94..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma
+++ /dev/null
@@ -1,115 +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/snalt_6.ma".
-include "basic_2/computation/lpxs_lleq.ma".
-include "basic_2/computation/lsx.ma".
-
-(* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
-
-(* alternative definition of lsx *)
-definition lsxa: ∀h. sd h → relation4 ynat term genv lenv ≝
-                 λh,o,l,T,G. SN … (lpxs h o G) (lleq l T).
-
-interpretation
-   "extended strong normalization (local environment) alternative"
-   'SNAlt h o l T G L = (lsxa h o T l G L).
-
-(* Basic eliminators ********************************************************)
-
-lemma lsxa_ind: ∀h,o,G,T,l. ∀R:predicate lenv.
-                (∀L1. G ⊢ ⬊⬊*[h, o, T, l] L1 →
-                      (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
-                      R L1
-                ) →
-                ∀L. G ⊢ ⬊⬊*[h, o, T, l] L → R L.
-#h #o #G #T #l #R #H0 #L1 #H elim H -L1
-/5 width=1 by lleq_sym, SN_intro/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma lsxa_intro: ∀h,o,G,L1,T,l.
-                  (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
-                  G ⊢ ⬊⬊*[h, o, T, l] L1.
-/5 width=1 by lleq_sym, SN_intro/ qed.
-
-fact lsxa_intro_aux: ∀h,o,G,L1,T,l.
-                     (∀L,L2. ⦃G, L⦄ ⊢ ➡*[h, o] L2 → L1 ≡[T, l] L → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
-                     G ⊢ ⬊⬊*[h, o, T, l] L1.
-/4 width=3 by lsxa_intro/ qed-.
-
-lemma lsxa_lleq_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊⬊*[h, o, T, l] L1 →
-                       ∀L2. L1 ≡[T, l] L2 → G ⊢ ⬊⬊*[h, o, T, l] L2.
-#h #o #T #G #L1 #l #H @(lsxa_ind … H) -L1
-#L1 #_ #IHL1 #L2 #HL12 @lsxa_intro
-#K2 #HLK2 #HnLK2 elim (lleq_lpxs_trans … HLK2 … HL12) -HLK2
-/5 width=4 by lleq_canc_sn, lleq_trans/
-qed-.
-
-lemma lsxa_lpxs_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊⬊*[h, o, T, l] L1 →
-                       ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → G ⊢ ⬊⬊*[h, o, T, l] L2.
-#h #o #T #G #L1 #l #H @(lsxa_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (lleq_dec T L1 L2 l) /3 width=4 by lsxa_lleq_trans/
-qed-.
-
-lemma lsxa_intro_lpx: ∀h,o,G,L1,T,l.
-                      (∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
-                      G ⊢ ⬊⬊*[h, o, T, l] L1.
-#h #o #G #L1 #T #l #IH @lsxa_intro_aux
-#L #L2 #H @(lpxs_ind_dx … H) -L
-[ #H destruct #H elim H //
-| #L0 #L elim (lleq_dec T L1 L l) /3 width=1 by/
-  #HnT #HL0 #HL2 #_ #HT #_ elim (lleq_lpx_trans … HL0 … HT) -L0
-  #L0 #HL10 #HL0 @(lsxa_lpxs_trans … HL2) -HL2
-  /5 width=3 by lsxa_lleq_trans, lleq_trans/
-]
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem lsx_lsxa: ∀h,o,G,L,T,l. G ⊢ ⬊*[h, o, T, l] L → G ⊢ ⬊⬊*[h, o, T, l] L.
-#h #o #G #L #T #l #H @(lsx_ind … H) -L
-/4 width=1 by lsxa_intro_lpx/
-qed.
-
-(* Main inversion lemmas ****************************************************)
-
-theorem lsxa_inv_lsx: ∀h,o,G,L,T,l. G ⊢ ⬊⬊*[h, o, T, l] L → G ⊢ ⬊*[h, o, T, l] L.
-#h #o #G #L #T #l #H @(lsxa_ind … H) -L
-/4 width=1 by lsx_intro, lpx_lpxs/
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma lsx_intro_alt: ∀h,o,G,L1,T,l.
-                     (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊*[h, o, T, l] L2) →
-                     G ⊢ ⬊*[h, o, T, l] L1.
-/6 width=1 by lsxa_inv_lsx, lsx_lsxa, lsxa_intro/ qed.
-
-lemma lsx_lpxs_trans: ∀h,o,G,L1,T,l. G ⊢ ⬊*[h, o, T, l] L1 →
-                      ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → G ⊢ ⬊*[h, o, T, l] L2.
-/4 width=3 by lsxa_inv_lsx, lsx_lsxa, lsxa_lpxs_trans/ qed-.
-
-(* Advanced eliminators *****************************************************)
-
-lemma lsx_ind_alt: ∀h,o,G,T,l. ∀R:predicate lenv.
-                   (∀L1. G ⊢ ⬊*[h, o, T, l] L1 →
-                         (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
-                         R L1
-                   ) →
-                   ∀L. G ⊢ ⬊*[h, o, T, l] L → R L.
-#h #o #G #T #l #R #IH #L #H @(lsxa_ind h o G T l … L)
-/4 width=1 by lsxa_inv_lsx, lsx_lsxa/
-qed-.