milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lsubr.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lsubr.etc
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/lsubr.etc
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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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-notation "hvbox( L1 ⓝ ⊑ break term 46 L2 )"
-   non associative with precedence 45
-   for @{ 'LRSubEqT $L1 $L2 }.
-
-include "basic_2/relocation/ldrop.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
-
-inductive lsubr: relation lenv ≝
-| lsubr_sort: ∀L. lsubr L (⋆)
-| lsubr_abbr: ∀L1,L2,V. lsubr L1 L2 → lsubr (L1. ⓓV) (L2.ⓓV)
-| lsubr_abst: ∀I,L1,L2,V1,V2. lsubr L1 L2 → lsubr (L1. ⓑ{I}V1) (L2. ⓛV2)
-.
-
-interpretation
-  "local environment refinement (substitution)"
-  'CrSubEq L1 L2 = (lsubr L1 L2).
-
-(* Basic properties *********************************************************)
-
-lemma lsubr_bind: ∀I,L1,L2,V. L1 ⊑ L2 → L1. ⓑ{I} V ⊑ L2.ⓑ{I} V.
-* /2 width=1/ qed.
-
-lemma lsubr_abbr: ∀I,L1,L2,V. L1 ⊑ L2 → L1. ⓓV ⊑ L2. ⓑ{I}V.
-* /2 width=1/ qed.
-
-lemma lsubr_refl: ∀L. L ⊑ L.
-#L elim L -L // /2 width=1/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsubr_inv_atom1_aux: ∀L1,L2. L1 ⊑ L2 → L1 = ⋆ → L2 = ⋆.
-#L1 #L2 * -L1 -L2 //
-[ #L1 #L2 #V #_ #H destruct
-| #I #L1 #L2 #V1 #V2 #_ #H destruct
-]
-qed-.
-
-lemma lsubr_inv_atom1: ∀L2. ⋆ ⊑ L2 → L2 = ⋆.
-/2 width=3 by lsubr_inv_atom1_aux/ qed-.
-
-fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⊑ L2 → ∀K2,W. L2 = K2.ⓓW →
-                          ∃∃K1. K1 ⊑ K2 & L1 = K1.ⓓW.
-#L1 #L2 * -L1 -L2
-[ #L #K2 #W #H destruct
-| #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3/
-| #I #L1 #L2 #V1 #V2 #_ #K2 #W #H destruct
-]
-qed-.
-
-lemma lsubr_inv_abbr2: ∀L1,K2,W. L1 ⊑ K2.ⓓW →
-                       ∃∃K1. K1 ⊑ K2 & L1 = K1.ⓓW.
-/2 width=3 by lsubr_inv_abbr2_aux/ qed-.
-
-fact lsubr_inv_abst2_aux: ∀L1,L2. L1 ⊑ L2 → ∀K2,W2. L2 = K2.ⓛW2 →
-                          ∃∃I,K1,W1. K1 ⊑ K2 & L1 = K1.ⓑ{I}W1.
-#L1 #L2 * -L1 -L2
-[ #L #K2 #W2 #H destruct
-| #L1 #L2 #V #_ #K2 #W2 #H destruct
-| #I #L1 #L2 #V1 #V2 #HL12 #K2 #W2 #H destruct /2 width=5/
-]
-qed-.
-
-lemma lsubr_inv_abst2: ∀L1,K2,W2. L1 ⊑ K2.ⓛW2 →
-                       ∃∃I,K1,W1. K1 ⊑ K2 & L1 = K1.ⓑ{I}W1.
-/2 width=4 by lsubr_inv_abst2_aux/ qed-.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma lsubr_fwd_length: ∀L1,L2. L1 ⊑ L2 → |L2| ≤ |L1|.
-#L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
-lemma lsubr_fwd_ldrop2_abbr: ∀L1,L2. L1 ⊑ L2 →
-                             ∀K2,W,i. ⇩[0, i] L2 ≡ K2. ⓓW →
-                             ∃∃K1. K1 ⊑ K2 & ⇩[0, i] L1 ≡ K1. ⓓW.
-#L1 #L2 #H elim H -L1 -L2
-[ #L #K2 #W #i #H
-  elim (ldrop_inv_atom1 … H) -H #H destruct
-| #L1 #L2 #V #HL12 #IHL12 #K2 #W #i #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /2 width=3/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 /3 width=3/
-  ]
-| #I #L1 #L2 #V1 #V2 #_ #IHL12 #K2 #W #i #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct
-  elim (IHL12 … HLK2) -IHL12 -HLK2 /3 width=3/
-]
-qed-.