milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / lsubr / lpss.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lpss.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lpss.etc
deleted file mode 100644 (file)
index 6d57e17..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lpss.etc
+++ /dev/null
@@ -1,85 +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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( T1 ⊢ ▶ * break term 46 T2 )"
-   non associative with precedence 45
-   for @{ 'PSubstStarSn $T1 $T2 }.
-
-include "basic_2/grammar/lpx_sn.ma".
-include "basic_2/substitution/cpss.ma".
-
-(* SN PARALLEL SUBSTITUTION FOR LOCAL ENVIRONMENTS **************************)
-
-(* Basic_1: includes: csubst1_bind *)
-definition lpss: relation lenv ≝ lpx_sn cpss. 
-
-interpretation "parallel substitution (local environment, sn variant)"
-   'PSubstStarSn L1 L2 = (lpss L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma lpss_inv_atom1: ∀L2. ⋆ ⊢ ▶* L2 → L2 = ⋆.
-/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
-
-lemma lpss_inv_pair1: ∀I,K1,V1,L2. K1. ⓑ{I} V1 ⊢ ▶* L2 →
-                      ∃∃K2,V2. K1 ⊢ ▶* K2 & K1 ⊢ V1 ▶* V2 & L2 = K2. ⓑ{I} V2.
-/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
-
-lemma lpss_inv_atom2: ∀L1. L1 ⊢ ▶* ⋆ → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
-
-lemma lpss_inv_pair2: ∀I,L1,K2,V2. L1 ⊢ ▶* K2. ⓑ{I} V2 →
-                       ∃∃K1,V1. K1 ⊢ ▶* K2 & K1 ⊢ V1 ▶* V2 & L1 = K1. ⓑ{I} V1.
-/2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was by definition: csubst1_refl *)
-lemma lpss_refl: ∀L. L ⊢ ▶* L.
-/2 width=1 by lpx_sn_refl/ qed.
-
-lemma lpss_pair: ∀I,K1,K2,V1,V2. K1 ⊢ ▶* K2 → K1 ⊢ V1 ▶* V2 →
-                 K1.ⓑ{I}V1 ⊢ ▶* K2.ⓑ{I}V2.
-/2 width=1/ qed.
-
-lemma lpss_append: ∀K1,K2. K1 ⊢ ▶* K2 → ∀L1,L2. L1 ⊢ ▶* L2 →
-                    L1 @@ K1 ⊢ ▶* L2 @@ K2.
-/3 width=1 by lpx_sn_append, cpss_append/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma lpss_fwd_length: ∀L1,L2. L1 ⊢ ▶* L2 → |L1| = |L2|.
-/2 width=2 by lpx_sn_fwd_length/ qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-lemma lpss_fwd_append1: ∀K1,L1,L. K1 @@ L1 ⊢ ▶* L →
-                        ∃∃K2,L2. K1 ⊢ ▶* K2 & L = K2 @@ L2.
-/2 width=2 by lpx_sn_fwd_append1/ qed-.
-
-lemma lpss_fwd_append2: ∀L,K2,L2. L ⊢ ▶* K2 @@ L2 →
-                        ∃∃K1,L1. K1 ⊢ ▶* K2 & L = K1 @@ L1.
-/2 width=2 by lpx_sn_fwd_append2/ qed-.
-
-(* Basic_1: removed theorems 28:
-            csubst0_clear_O csubst0_drop_lt csubst0_drop_gt csubst0_drop_eq
-            csubst0_clear_O_back csubst0_clear_S csubst0_clear_trans
-            csubst0_drop_gt_back csubst0_drop_eq_back csubst0_drop_lt_back
-            csubst0_gen_sort csubst0_gen_head csubst0_getl_ge csubst0_getl_lt
-            csubst0_gen_S_bind_2 csubst0_getl_ge_back csubst0_getl_lt_back
-            csubst0_snd_bind csubst0_fst_bind csubst0_both_bind
-            csubst1_head csubst1_flat csubst1_gen_head
-            csubst1_getl_ge csubst1_getl_lt csubst1_getl_ge_back getl_csubst1
-            fsubst0_gen_base
-*)