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[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / ltpss_ldrop.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_ldrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_ldrop.ma
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--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss_ldrop.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/ltps_ldrop.ma".
-include "Basic_2/unfold/ltpss.ma".
-
-(* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************)
-
-lemma ltpss_ldrop_conf_ge: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
-                           ∀L2,e2. ⇩[0, e2] L0 ≡ L2 →
-                           d1 + e1 ≤ e2 → ⇩[0, e2] L1 ≡ L2.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1 // /3 width=6/
-qed.
-
-lemma ltpss_ldrop_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
-                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 →
-                            d1 + e1 ≤ e2 → ⇩[0, e2] L1 ≡ L2.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0 // /3 width=6/
-qed.
-
-lemma ltpss_ldrop_conf_be: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
-                           ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                           ∃∃L. L2 [0, d1 + e1 - e2] ▶* L & ⇩[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1
-[ /2 width=3/
-| #L #L1 #_ #HL1 #IHL #L2 #e2 #HL02 #Hd1e2 #He2de1
-  elim (IHL … HL02 Hd1e2 He2de1) -L0 #L0 #HL20 #HL0
-  elim (ltps_ldrop_conf_be … HL1 … HL0 Hd1e2 He2de1) -L /3 width=3/
-]
-qed.
-
-lemma ltpss_ldrop_trans_be: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
-                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                            ∃∃L. L [0, d1 + e1 - e2] ▶* L2 & ⇩[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0
-[ /2 width=3/
-| #L #L0 #_ #HL0 #IHL #L2 #e2 #HL02 #Hd1e2 #He2de1
-  elim (ltps_ldrop_trans_be … HL0 … HL02 Hd1e2 He2de1) -L0 #L0 #HL02 #HL0
-  elim (IHL … HL0 Hd1e2 He2de1) -L /3 width=3/
-]
-qed.
-
-lemma ltpss_ldrop_conf_le: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
-                           ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                           ∃∃L. L2 [d1 - e2, e1] ▶* L & ⇩[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1
-[ /2 width=3/
-| #L #L1 #_ #HL1 #IHL #L2 #e2 #HL02 #He2d1
-  elim (IHL … HL02 He2d1) -L0 #L0 #HL20 #HL0
-  elim (ltps_ldrop_conf_le … HL1 … HL0 He2d1) -L /3 width=3/
-]
-qed.
-
-lemma ltpss_ldrop_trans_le: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
-                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                            ∃∃L. L [d1 - e2, e1] ▶* L2 & ⇩[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0
-[ /2 width=3/
-| #L #L0 #_ #HL0 #IHL #L2 #e2 #HL02 #He2d1
-  elim (ltps_ldrop_trans_le … HL0 … HL02 He2d1) -L0 #L0 #HL02 #HL0
-  elim (IHL … HL0 He2d1) -L /3 width=3/
-]
-qed.