milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn.etc
deleted file mode 100644 (file)
index f6b5450..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn.etc
+++ /dev/null
@@ -1,110 +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( h ⊢ break term 46 L1 : ⊑ [ ] break term 46 L2 )"
-   non associative with precedence 45
-   for @{ 'StratifiedCrSubEqN $h $L1 $L2 }.
-
-include "basic_2/dynamic/snta.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE TYPE ASSIGNMENT *******)
-
-(* Note: may not be transitive *)
-inductive lsubsn (h:sh): relation lenv ≝
-| lsubsn_atom: lsubsn h (⋆) (⋆)
-| lsubsn_pair: ∀I,L1,L2,W. lsubsn h L1 L2 →
-               lsubsn h (L1. ⓑ{I} W) (L2. ⓑ{I} W)
-| lsubsn_abbr: ∀L1,L2,V,W,l. ⦃h, L1⦄ ⊢ V :[l+1] W → ⦃h, L2⦄ ⊢ V :[l+1] W →
-               lsubsn h L1 L2 → lsubsn h (L1. ⓓV) (L2. ⓛW)
-.
-
-interpretation
-  "local environment refinement (stratified native type assigment)"
-  'StratifiedCrSubEqN h L1 L2 = (lsubsn h L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsubsn_inv_atom1_aux: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 → L1 = ⋆ → L2 = ⋆.
-#h #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #l #_ #_ #_ #H destruct
-]
-qed.
-
-lemma lsubsn_inv_atom1: ∀h,L2. h ⊢ ⋆ :⊑[] L2 → L2 = ⋆.
-/2 width=5/ qed-.
-
-fact lsubsn_inv_pair1_aux: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
-                           ∀I,K1,V. L1 = K1. ⓑ{I} V →
-                           (∃∃K2. h ⊢ K1 :⊑[] K2 & L2 = K2. ⓑ{I} V) ∨
-                           ∃∃K2,W,l. ⦃h, K1⦄ ⊢ V :[l+1] W & ⦃h, K2⦄ ⊢ V :[l+1] W &
-                                     h ⊢ K1 :⊑[] K2 & L2 = K2. ⓛW & I = Abbr.
-#h #L1 #L2 * -L1 -L2
-[ #I #K1 #V #H destruct
-| #J #L1 #L2 #V #HL12 #I #K1 #W #H destruct /3 width=3/
-| #L1 #L2 #V #W #l #H1VW #H2VW #HL12 #I #K1 #V1 #H destruct /3 width=7/
-]
-qed.
-
-lemma lsubsn_inv_pair1: ∀h,I,K1,L2,V. h ⊢ K1. ⓑ{I} V :⊑[] L2 →
-                        (∃∃K2. h ⊢ K1 :⊑[] K2 & L2 = K2. ⓑ{I} V) ∨
-                        ∃∃K2,W,l. ⦃h, K1⦄ ⊢ V :[l+1] W & ⦃h, K2⦄ ⊢ V :[l+1] W &
-                                  h ⊢ K1 :⊑[] K2 & L2 = K2. ⓛW & I = Abbr.
-/2 width=3/ qed-.
-
-fact lsubsn_inv_atom2_aux: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 → L2 = ⋆ → L1 = ⋆.
-#h #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #l #_ #_ #_ #H destruct
-]
-qed.
-
-lemma lsubsn_inv_atom2: ∀h,L1. h ⊢ L1 :⊑[] ⋆ → L1 = ⋆.
-/2 width=5/ qed-.
-
-fact lsubsn_inv_pair2_aux: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
-                           ∀I,K2,W. L2 = K2. ⓑ{I} W →
-                           (∃∃K1. h ⊢ K1 :⊑[] K2 & L1 = K1. ⓑ{I} W) ∨
-                           ∃∃K1,V,l. ⦃h, K1⦄ ⊢ V :[l+1] W & ⦃h, K2⦄ ⊢ V :[l+1] W &
-                                     h ⊢ K1 :⊑[] K2 & L1 = K1. ⓓV & I = Abst.
-#h #L1 #L2 * -L1 -L2
-[ #I #K2 #W #H destruct
-| #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
-| #L1 #L2 #V #W #l #H1VW #H2VW #HL12 #I #K2 #W2 #H destruct /3 width=7/
-]
-qed.
-
-lemma lsubsn_inv_pair2: ∀h,I,L1,K2,W. h ⊢ L1 :⊑[] K2. ⓑ{I} W →
-                        (∃∃K1. h ⊢ K1 :⊑[] K2 & L1 = K1. ⓑ{I} W) ∨
-                        ∃∃K1,V,l. ⦃h, K1⦄ ⊢ V :[l+1] W & ⦃h, K2⦄ ⊢ V :[l+1] W &
-                                  h ⊢ K1 :⊑[] K2 & L1 = K1. ⓓV & I = Abst.
-/2 width=3/ qed-.
-
-(* Basic_forward lemmas *****************************************************)
-
-lemma lsubsn_fwd_lsubs1: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 → L1 ≼[0, |L1|] L2.
-#h #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
-lemma lsubsn_fwd_lsubs2: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 → L1 ≼[0, |L2|] L2.
-#h #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma lsubsn_refl: ∀h,L. h ⊢ L :⊑[] L.
-#h #L elim L -L // /2 width=1/
-qed.