- transitivity of parallel telescopic substitution closed!

[helm.git] / matita / matita / lib / lambda-delta / substitution / lift_fun.ma

diff --git a/matita/matita/lib/lambda-delta/substitution/lift_fun.ma b/matita/matita/lib/lambda-delta/substitution/lift_fun.ma
deleted file mode 100644 (file)
index 58d718f..0000000
--- a/matita/matita/lib/lambda-delta/substitution/lift_fun.ma
+++ /dev/null
@@ -1,61 +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 "lambda-delta/substitution/lift_defs.ma".
-
-(* RELOCATION ***************************************************************)
-
-(* Functional properties ****************************************************)
-
-lemma lift_total: ∀T1,d,e. ∃T2. ↑[d,e] T1 ≡ T2.
-#T1 elim T1 -T1
-[ /2/
-| #i #d #e elim (lt_or_ge i d) /3/
-| * #I #V1 #T1 #IHV1 #IHT1 #d #e
-  elim (IHV1 d e) -IHV1 #V2 #HV12
-  [ elim (IHT1 (d+1) e) -IHT1 /3/
-  | elim (IHT1 d e) -IHT1 /3/
-  ]
-]
-qed.
-
-lemma lift_mono:  ∀d,e,T,U1. ↑[d,e] T ≡ U1 → ∀U2. ↑[d,e] T ≡ U2 → U1 = U2.
-#d #e #T #U1 #H elim H -H d e T U1
-[ #k #d #e #X #HX
-  lapply (lift_inv_sort1 … HX) -HX //
-| #i #d #e #Hid #X #HX 
-  lapply (lift_inv_lref1_lt … HX ?) -HX //
-| #i #d #e #Hdi #X #HX 
-  lapply (lift_inv_lref1_ge … HX ?) -HX //
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_bind1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_flat1 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
-]
-qed.
-
-lemma lift_inj:  ∀d,e,T1,U. ↑[d,e] T1 ≡ U → ∀T2. ↑[d,e] T2 ≡ U → T1 = T2.
-#d #e #T1 #U #H elim H -H d e T1 U
-[ #k #d #e #X #HX
-  lapply (lift_inv_sort2 … HX) -HX //
-| #i #d #e #Hid #X #HX 
-  lapply (lift_inv_lref2_lt … HX ?) -HX //
-| #i #d #e #Hdi #X #HX 
-  lapply (lift_inv_lref2_ge … HX ?) -HX /2/
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_bind2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
-| #I #V1 #V2 #T1 #T2 #d #e #_ #_ #IHV12 #IHT12 #X #HX
-  elim (lift_inv_flat2 … HX) -HX #V #T #HV1 #HT1 #HX destruct -X /3/
-]
-qed.