- some refactoring and minor additions

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lifts_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lifts_lift.ma
deleted file mode 100644 (file)
index 9ec4d7e..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lifts_lift.ma
+++ /dev/null
@@ -1,59 +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/relocation/lift_lift.ma".
-include "basic_2/substitution/gr2_minus.ma".
-include "basic_2/substitution/lifts.ma".
-
-(* GENERIC TERM RELOCATION **************************************************)
-
-(* Properties concerning basic term relocation ******************************)
-
-(* Basic_1: was: lift1_xhg (right to left) *)
-lemma lifts_lift_trans_le: ∀T1,T,des. ⇧*[des] T1 ≡ T → ∀T2. ⇧[0, 1] T ≡ T2 →
-                           ∃∃T0. ⇧[0, 1] T1 ≡ T0 & ⇧*[des + 1] T0 ≡ T2.
-#T1 #T #des #H elim H -T1 -T -des
-[ /2 width=3/
-| #T1 #T3 #T #des #d #e #HT13 #_ #IHT13 #T2 #HT2
-  elim (IHT13 … HT2) -T #T #HT3 #HT2
-  elim (lift_trans_le … HT13 … HT3) -T3 // /3 width=5/
-]
-qed-.
-
-(* Basic_1: was: lift1_free (right to left) *)
-lemma lifts_lift_trans: ∀des,i,i0. @⦃i, des⦄ ≡ i0 →
-                        ∀des0. des + 1 ▭ i + 1 ≡ des0 + 1 →
-                        ∀T1,T0. ⇧*[des0] T1 ≡ T0 →
-                        ∀T2. ⇧[O, i0 + 1] T0 ≡ T2 →
-                        ∃∃T. ⇧[0, i + 1] T1 ≡ T & ⇧*[des] T ≡ T2.
-#des elim des -des normalize
-[ #i #x #H1 #des0 #H2 #T1 #T0 #HT10 #T2
-  <(at_inv_nil … H1) -x #HT02
-  lapply (minuss_inv_nil1 … H2) -H2 #H
-  >(pluss_inv_nil2 … H) in HT10; -des0 #H
-  >(lifts_inv_nil … H) -T1 /2 width=3/
-| #d #e #des #IHdes #i #i0 #H1 #des0 #H2 #T1 #T0 #HT10 #T2 #HT02
-  elim (at_inv_cons … H1) -H1 * #Hid #Hi0
-  [ elim (minuss_inv_cons1_lt … H2) -H2 [2: /2 width=1/ ] #des1 #Hdes1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
-    elim (pluss_inv_cons2 … H) -H #des2 #H1 #H2 destruct
-    elim (lifts_inv_cons … HT10) -HT10 #T >minus_plus #HT1 #HT0
-    elim (IHdes … Hi0 … Hdes1 … HT0 … HT02) -IHdes -Hi0 -Hdes1 -T0 #T0 #HT0 #HT02
-    elim (lift_trans_le … HT1 … HT0) -T /2 width=1/ #T #HT1 <plus_minus_m_m /2 width=1/ /3 width=5/
-  | >commutative_plus in Hi0; #Hi0
-    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1/ ] <associative_plus #Hdes0
-    elim (IHdes … Hi0 … Hdes0 … HT10 … HT02) -IHdes -Hi0 -Hdes0 -T0 #T0 #HT0 #HT02
-    elim (lift_split … HT0 d (i+1)) -HT0 /2 width=1/ /3 width=5/
-  ]
-]
-qed-.