- updated equivalence on referred entries: it nust be degree-based

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_new / drops / drops_append.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops_append.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops_append.etc
deleted file mode 100644 (file)
index d134fe7..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_new/drops/drops_append.etc
+++ /dev/null
@@ -1,65 +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/grammar/lenv_append.ma".
-include "basic_2/substitution/drop.ma".
-
-(* DROPPING *****************************************************************)
-
-(* Properties on append for local environments ******************************)
-
-fact drop_O1_append_sn_le_aux: ∀L1,L2,s,l,m. ⬇[s, l, m] L1 ≡ L2 →
-                               l = 0 → m ≤ |L1| →
-                               ∀L. ⬇[s, 0, m] L @@ L1 ≡ L @@ L2.
-#L1 #L2 #s #l #m #H elim H -L1 -L2 -l -m //
-[ #l #m #_ #_ #H >(yle_inv_O2 … H) -m //
-| /4 width=1 by drop_drop, yle_inv_succ/
-| #I #L1 #L2 #V1 #V2 #l #m #_ #_ #_ #H elim (ysucc_inv_O_dx … H)
-]
-qed-.
-
-lemma drop_O1_append_sn_le: ∀L1,L2,s,m. ⬇[s, yinj 0, m] L1 ≡ L2 → m ≤ |L1| →
-                            ∀L. ⬇[s, 0, m] L @@ L1 ≡ L @@ L2.
-/2 width=3 by drop_O1_append_sn_le_aux/ qed.
-
-(* Inversion lemmas on append for local environments ************************)
-
-lemma drop_O1_inv_append1_ge: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 @@ L2 ≡ K →
-                              ∀m0. |L2| + m0 = m → ⬇[s, 0, m0] L1 ≡ K.
-#K #L1 #L2 elim L2 -L2
-[ #s #m #H #m0 >yplus_O1 #H0 destruct //
-| #L2 #I #V #IHL2 #s #m #H #m0 >yplus_succ1
-  #H0 elim (drop_inv_O1_pair1 … H) -H * #Hm #HL12 destruct
-  [ elim (ysucc_inv_O_dx … Hm)
-  | /2 width=3 by/
-  ]
-]
-qed-.
-
-lemma drop_O1_inv_append1_le: ∀K,L1,L2,s,m. ⬇[s, 0, m] L1 @@ L2 ≡ K → m ≤ |L2| →
-                              ∀K2. ⬇[s, 0, m] L2 ≡ K2 → K = L1 @@ K2.
-#K #L1 #L2 elim L2 -L2
-[ #s #m #H1 #H2 #K2 #H3 lapply (yle_inv_O2 … H2) -H2
-  #H2 elim (drop_inv_atom1 … H3) -H3 #H3 #_ destruct
-  >(drop_inv_O2 … H1) -H1 //
-| #L2 #I #V #IHL2 #s #m @(ynat_ind … m) -m [ -IHL2 || -IHL2 ]
-  [ #H1 #_ #K2 #H2
-    lapply (drop_inv_O2 … H1) -H1 #H1
-    lapply (drop_inv_O2 … H2) -H2 #H2 destruct //
-  | /3 width=7 by drop_inv_drop1, yle_inv_succ/
-  | #_ #H lapply (yle_inv_Y1 … H) -H
-    #H elim (ylt_yle_false (|L2.ⓑ{I}V|) (∞)) //
-  ]
-]
-qed-.