milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / llpx / llsx_llpxs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llsx_llpxs.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llsx_llpxs.etc
new file mode 100644 (file)
index 0000000..af37a37
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llsx_llpxs.etc
@@ -0,0 +1,66 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/computation/llpxs_llpxs.ma".
+include "basic_2/computation/llsx_alt.ma".
+
+(* SN EXTENDED STRONGLY NORMALIZING LOCAL ENVIRONMENTS **********************)
+
+(* Advanced properties ******************************************************)
+
+fact llsx_bind_llpxs_aux: ∀h,g,a,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 →
+                          ∀Y,T. G ⊢ ⋕⬊*[h, g, T, ⫯d] Y →
+                          ∀L2. Y = L2.ⓑ{I}V → ⦃G, L1⦄ ⊢ ➡*[h, g, ⓑ{a,I}V.T, d] L2 →
+                          G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L2.
+#h #g #a #I #G #L1 #V #d #H @(llsx_ind_alt … H) -L1
+#L1 #HL1 #IHL1 #Y #T #H @(llsx_ind_alt … H) -Y
+#Y #HY #IHY #L2 #H #HL12 destruct @llsx_intro_alt
+#L0 #HL20 lapply (llpxs_fwd_bind_dx … HL20)
+lapply (llpxs_trans … HL12 … HL20)
+#HL10 #HT #H elim (nlleq_inv_bind … H) -H [ -HL1 -IHY | -HY -IHL1 ]
+[ #HnV elim (lleq_dec V L1 L2 d)
+  [  -HL20 #HV @(IHL1 … L0)
+     /3 width=4 by llsx_llpxs_trans, llpxs_fwd_bind_sn, lleq_canc_sn/ (**) (* full auto too slow *)
+  | -HnV -HL10
+     /3 width=4 by llsx_llpxs_trans, llpxs_fwd_bind_sn/
+  ]
+| /3 width=4 by/
+]
+qed-.
+
+lemma llsx_bind: ∀h,g,a,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L →
+                 ∀T. G ⊢ ⋕⬊*[h, g, T, ⫯d] L.ⓑ{I}V →
+                 G ⊢ ⋕⬊*[h, g, ⓑ{a,I}V.T, d] L.
+/2 width=3 by llsx_bind_llpxs_aux/ qed.
+
+lemma llsx_flat_llpxs: ∀h,g,I,G,L1,V,d. G ⊢ ⋕⬊*[h, g, V, d] L1 →
+                       ∀L2,T. G ⊢ ⋕⬊*[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, ⓕ{I}V.T, d] L2 →
+                       G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L2.
+#h #g #I #G #L1 #V #d #H @(llsx_ind_alt … H) -L1
+#L1 #HL1 #IHL1 #L2 #T #H @(llsx_ind_alt … H) -L2
+#L2 #HL2 #IHL2 #HL12 @llsx_intro_alt
+#L0 #HL20 lapply (llpxs_fwd_flat_dx … HL20)
+lapply (llpxs_trans … HL12 … HL20)
+#HL10 #HT #H elim (nlleq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
+[ #HnV elim (lleq_dec V L1 L2 d)
+  [ #HV @(IHL1 … L0) /3 width=3 by llsx_llpxs_trans, llpxs_fwd_flat_sn, lleq_canc_sn/ (**) (* full auto too slow: 47s *)
+  | -HnV -HL10 /3 width=4 by llsx_llpxs_trans, llpxs_fwd_flat_sn/
+  ]
+| /3 width=1 by/
+]
+qed-.
+
+lemma llsx_flat: ∀h,g,I,G,L,V,d. G ⊢ ⋕⬊*[h, g, V, d] L →
+                 ∀T. G ⊢ ⋕⬊*[h, g, T, d] L → G ⊢ ⋕⬊*[h, g, ⓕ{I}V.T, d] L.
+/2 width=3 by llsx_flat_llpxs/ qed.