- the relocation properties of cpr are closed!

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / drop_drop.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/drop_drop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/drop_drop.ma
deleted file mode 100644 (file)
index b8a790f..0000000
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/drop_drop.ma
+++ /dev/null
@@ -1,127 +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/substitution/lift_lift.ma".
-include "Basic_2/substitution/drop.ma".
-
-(* DROPPING *****************************************************************)
-
-(* Main properties **********************************************************)
-
-(* Basic_1: was: drop_mono *)
-theorem drop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
-                   ∀L2. ↓[d, e] L ≡ L2 → L1 = L2.
-#d #e #L #L1 #H elim H -H d e L L1
-[ #d #e #L2 #H
-  >(drop_inv_atom1 … H) -H L2 //
-| #K #I #V #L2 #HL12
-   <(drop_inv_refl … HL12) -HL12 L2 //
-| #L #K #I #V #e #_ #IHLK #L2 #H
-  lapply (drop_inv_drop1 … H ?) -H /2/
-| #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H
-  elim (drop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct -X
-  >(lift_inj … HVT1 … HVT2) -HVT1 HVT2
-  >(IHLK1 … HLK2) -IHLK1 HLK2 // 
-]
-qed.
-
-(* Basic_1: was: drop_conf_ge *)
-theorem drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
-                      ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
-                      ↓[0, e2 - e1] L1 ≡ L2.
-#d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
-[ #d #e #e2 #L2 #H
-  >(drop_inv_atom1 … H) -H L2 //
-| //
-| #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
-  lapply (drop_inv_drop1 … H ?) -H /2/ #HL2
-  <minus_plus_comm /3/
-| #L #K #I #V1 #V2 #d #e #_ #_ #IHLK #e2 #L2 #H #Hdee2
-  lapply (transitive_le 1 … Hdee2) // #He2
-  lapply (drop_inv_drop1 … H ?) -H // -He2 #HL2
-  lapply (transitive_le (1 + e) … Hdee2) // #Hee2
-  @drop_drop_lt >minus_minus_comm /3/ (**) (* explicit constructor *)
-]
-qed.
-
-(* Basic_1: was: drop_conf_lt *)
-theorem drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
-                      ∀e2,K2,I,V2. ↓[0, e2] L ≡ K2. 𝕓{I} V2 →
-                      e2 < d1 → let d ≝ d1 - e2 - 1 in
-                      ∃∃K1,V1. ↓[0, e2] L1 ≡ K1. 𝕓{I} V1 &
-                               ↓[d, e1] K2 ≡ K1 & ↑[d, e1] V1 ≡ V2.
-#d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
-[ #d #e #e2 #K2 #I #V2 #H
-  lapply (drop_inv_atom1 … H) -H #H destruct
-| #L #I #V #e2 #K2 #J #V2 #_ #H
-  elim (lt_zero_false … H)
-| #L1 #L2 #I #V #e #_ #_ #e2 #K2 #J #V2 #_ #H
-  elim (lt_zero_false … H)
-| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #K2 #J #V #H #He2d
-  elim (drop_inv_O1 … H) -H *
-  [ -IHL12 He2d #H1 #H2 destruct -e2 K2 J V /2 width=5/
-  | -HL12 -HV12 #He #HLK
-    elim (IHL12 … HLK ?) -IHL12 HLK [ <minus_minus /3 width=5/ | /2/ ] (**) (* a bit slow *)
-  ]
-]
-qed.
-
-(* Basic_1: was: drop_trans_le *)
-theorem drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
-                       ∀e2,L2. ↓[0, e2] L ≡ L2 → e2 ≤ d1 →
-                       ∃∃L0. ↓[0, e2] L1 ≡ L0 & ↓[d1 - e2, e1] L0 ≡ L2.
-#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
-[ #d #e #e2 #L2 #H
-  >(drop_inv_atom1 … H) -H L2 /2/
-| #K #I #V #e2 #L2 #HL2 #H
-  lapply (le_O_to_eq_O … H) -H #H destruct -e2 /2/
-| #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H
-  lapply (le_O_to_eq_O … H) -H #H destruct -e2;
-  elim (IHL12 … HL2 ?) -IHL12 HL2 // #L0 #H #HL0
-  lapply (drop_inv_refl … H) -H #H destruct -L1 /3 width=5/
-| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #L #H #He2d
-  elim (drop_inv_O1 … H) -H *
-  [ -He2d IHL12 #H1 #H2 destruct -e2 L /3 width=5/
-  | -HL12 HV12 #He2 #HL2
-    elim (IHL12 … HL2 ?) -IHL12 HL2 L2
-    [ >minus_le_minus_minus_comm // /3/ | /2/ ]
-  ]
-]
-qed.
-
-(* Basic_1: was: drop_trans_ge *)
-theorem drop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
-                       ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 ≤ e2 → ↓[0, e1 + e2] L1 ≡ L2.
-#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
-[ #d #e #e2 #L2 #H
-  >(drop_inv_atom1 … H) -H L2 //
-| //
-| /3/
-| #L1 #L2 #I #V1 #V2 #d #e #H_ #_ #IHL12 #e2 #L #H #Hde2
-  lapply (lt_to_le_to_lt 0 … Hde2) // #He2
-  lapply (lt_to_le_to_lt … (e + e2) He2 ?) // #Hee2
-  lapply (drop_inv_drop1 … H ?) -H // #HL2
-  @drop_drop_lt // >le_plus_minus // @IHL12 /2/ (**) (* explicit constructor *)
-]
-qed.
-
-theorem drop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
-                            ↓[d1, e1] L1 ≡ L → ↓[0, e2] L ≡ L2 → d1 ≤ e2 →
-                            ↓[0, e2 + e1] L1 ≡ L2.
-#e1 #e1 #e2 >commutative_plus /2 width=5/
-qed.
-
-(* Basic_1: was: drop_conf_rev *)
-axiom drop_div: ∀e1,L1,L. ↓[0, e1] L1 ≡ L → ∀e2,L2. ↓[0, e2] L2 ≡ L →
-                ∃∃L0. ↓[0, e1] L0 ≡ L2 & ↓[e1, e2] L0 ≡ L1.