- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / drop_leq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_leq.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_leq.ma
deleted file mode 100644 (file)
index d04c13b..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/drop_leq.ma
+++ /dev/null
@@ -1,92 +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/leq_leq.ma".
-include "basic_2/substitution/drop.ma".
-
-(* BASIC SLICING FOR LOCAL ENVIRONMENTS *************************************)
-
-definition dedropable_sn: predicate (relation lenv) ≝
-                          λR. ∀L1,K1,s,d,e. ⬇[s, d, e] L1 ≡ K1 → ∀K2. R K1 K2 →
-                          ∃∃L2. R L1 L2 & ⬇[s, d, e] L2 ≡ K2 & L1 ⩬[d, e] L2.
-
-(* Properties on equivalence ************************************************)
-
-lemma leq_drop_trans_be: ∀L1,L2,d,e. L1 ⩬[d, e] L2 →
-                         ∀I,K2,W,s,i. ⬇[s, 0, i] L2 ≡ K2.ⓑ{I}W →
-                         d ≤ i → i < d + e →
-                         ∃∃K1. K1 ⩬[0, ⫰(d+e-i)] K2 & ⬇[s, 0, i] L1 ≡ K1.ⓑ{I}W.
-#L1 #L2 #d #e #H elim H -L1 -L2 -d -e
-[ #d #e #J #K2 #W #s #i #H
-  elim (drop_inv_atom1 … H) -H #H destruct
-| #I1 #I2 #L1 #L2 #V1 #V2 #_ #_ #J #K2 #W #s #i #_ #_ #H
-  elim (ylt_yle_false … H) //
-| #I #L1 #L2 #V #e #HL12 #IHL12 #J #K2 #W #s #i #H #_ >yplus_O1
-  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK1 [ -IHL12 | -HL12 ]
-  [ #_ destruct >ypred_succ
-    /2 width=3 by drop_pair, ex2_intro/
-  | lapply (ylt_inv_O1 i ?) /2 width=1 by ylt_inj/
-    #H <H -H #H lapply (ylt_inv_succ … H) -H
-    #Hie elim (IHL12 … HLK1) -IHL12 -HLK1 // -Hie
-    >yminus_succ <yminus_inj /3 width=3 by drop_drop_lt, ex2_intro/
-  ]
-| #I1 #I2 #L1 #L2 #V1 #V2 #d #e #_ #IHL12 #J #K2 #W #s #i #HLK2 #Hdi
-  elim (yle_inv_succ1 … Hdi) -Hdi
-  #Hdi #Hi <Hi >yplus_succ1 #H lapply (ylt_inv_succ … H) -H
-  #Hide lapply (drop_inv_drop1_lt … HLK2 ?) -HLK2 /2 width=1 by ylt_O/
-  #HLK1 elim (IHL12 … HLK1) -IHL12 -HLK1 <yminus_inj >yminus_SO2
-  /4 width=3 by ylt_O, drop_drop_lt, ex2_intro/
-]
-qed-.
-
-lemma leq_drop_conf_be: ∀L1,L2,d,e. L1 ⩬[d, e] L2 →
-                        ∀I,K1,W,s,i. ⬇[s, 0, i] L1 ≡ K1.ⓑ{I}W →
-                        d ≤ i → i < d + e →
-                        ∃∃K2. K1 ⩬[0, ⫰(d+e-i)] K2 & ⬇[s, 0, i] L2 ≡ K2.ⓑ{I}W.
-#L1 #L2 #d #e #HL12 #I #K1 #W #s #i #HLK1 #Hdi #Hide
-elim (leq_drop_trans_be … (leq_sym … HL12) … HLK1) // -L1 -Hdi -Hide
-/3 width=3 by leq_sym, ex2_intro/
-qed-.
-
-lemma drop_O1_ex: ∀K2,i,L1. |L1| = |K2| + i →
-                  ∃∃L2. L1 ⩬[0, i] L2 & ⬇[i] L2 ≡ K2.
-#K2 #i @(nat_ind_plus … i) -i
-[ /3 width=3 by leq_O2, ex2_intro/
-| #i #IHi #Y #Hi elim (drop_O1_lt (Ⓕ) Y 0) //
-  #I #L1 #V #H lapply (drop_inv_O2 … H) -H #H destruct
-  normalize in Hi; elim (IHi L1) -IHi
-  /3 width=5 by drop_drop, leq_pair, injective_plus_l, ex2_intro/
-]
-qed-.
-
-lemma dedropable_sn_TC: ∀R. dedropable_sn R → dedropable_sn (TC … R).
-#R #HR #L1 #K1 #s #d #e #HLK1 #K2 #H elim H -K2
-[ #K2 #HK12 elim (HR … HLK1 … HK12) -HR -K1
-  /3 width=4 by inj, ex3_intro/
-| #K #K2 #_ #HK2 * #L #H1L1 #HLK #H2L1 elim (HR … HLK … HK2) -HR -K
-  /3 width=6 by leq_trans, step, ex3_intro/
-]
-qed-.
-
-(* Inversion lemmas on equivalence ******************************************)
-
-lemma drop_O1_inj: ∀i,L1,L2,K. ⬇[i] L1 ≡ K → ⬇[i] L2 ≡ K → L1 ⩬[i, ∞] L2.
-#i @(nat_ind_plus … i) -i
-[ #L1 #L2 #K #H <(drop_inv_O2 … H) -K #H <(drop_inv_O2 … H) -L1 //
-| #i #IHi * [2: #L1 #I1 #V1 ] * [2,4: #L2 #I2 #V2 ] #K #HLK1 #HLK2 //
-  lapply (drop_fwd_length … HLK1)
-  <(drop_fwd_length … HLK2) [ /4 width=5 by drop_inv_drop1, leq_succ/ ]
-  normalize <plus_n_Sm #H destruct
-]
-qed-.