refactoring to park the notions:

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
deleted file mode 100644 (file)
index 81dc6e7..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_lpx.ma
+++ /dev/null
@@ -1,63 +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/multiple/lleq_lleq.ma".
-include "basic_2/reduction/lpx_lleq.ma".
-include "basic_2/computation/lsx.ma".
-
-(* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
-
-(* Advanced properties ******************************************************)
-
-lemma lsx_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 @(lsx_ind … H) -L1
-#L1 #_ #IHL1 #L2 #HL12 @lsx_intro
-#K2 #HLK2 #HnLK2 elim (lleq_lpx_trans … HLK2 … HL12) -HLK2
-/5 width=4 by lleq_canc_sn, lleq_trans/
-qed-.
-
-lemma lsx_lpx_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 @(lsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (lleq_dec T L1 L2 l) /3 width=4 by lsx_lleq_trans/
-qed-.
-
-lemma lsx_lreq_conf: ∀h,o,G,L1,T,l. G ⊢ ⬊*[h, o, T, l] L1 →
-                    ∀L2. L1 ⩬[l, ∞] L2 → G ⊢ ⬊*[h, o, T, l] L2.
-#h #o #G #L1 #T #l #H @(lsx_ind … H) -L1
-#L1 #_ #IHL1 #L2 #HL12 @lsx_intro
-#L3 #HL23 #HnL23 elim (lreq_lpx_trans_lleq … HL12 … HL23) -HL12 -HL23
-#L0 #HL03 #HL10 #H elim (H T) -H /4 width=4 by/
-qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-lemma lsx_fwd_bind_dx: ∀h,o,a,I,G,L,V,T,l. G ⊢ ⬊*[h, o, ⓑ{a,I}V.T, l] L →
-                       G ⊢ ⬊*[h, o, T, ⫯l] L.ⓑ{I}V.
-#h #o #a #I #G #L #V1 #T #l #H @(lsx_ind … H) -L
-#L1 #_ #IHL1 @lsx_intro
-#Y #H #HT elim (lpx_inv_pair1 … H) -H
-#L2 #V2 #HL12 #_ #H destruct
-@(lsx_lreq_conf … (L2.ⓑ{I}V1)) /2 width=1 by lreq_succ/
-@IHL1 // #H @HT -IHL1 -HL12 -HT
-@(lleq_lreq_trans … (L2.ⓑ{I}V1))
-/2 width=2 by lleq_fwd_bind_dx, lreq_succ/
-qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma lsx_inv_bind: ∀h,o,a,I,G,L,V,T,l. G ⊢ ⬊*[h, o, ⓑ{a, I}V.T, l] L →
-                    G ⊢ ⬊*[h, o, V, l] L ∧ G ⊢ ⬊*[h, o, T, ⫯l] L.ⓑ{I}V.
-/3 width=4 by lsx_fwd_bind_sn, lsx_fwd_bind_dx, conj/ qed-.