refactoring to park the notions:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpx_drop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_drop.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_drop.ma
deleted file mode 100644 (file)
index 6473e73..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_drop.ma
+++ /dev/null
@@ -1,78 +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/lpx_sn_drop.ma".
-include "basic_2/reduction/cpx_lift.ma".
-include "basic_2/reduction/lpx.ma".
-
-(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
-
-(* Properties on local environment slicing ***********************************)
-
-lemma lpx_drop_conf: ∀h,o,G. dropable_sn (lpx h o G).
-/3 width=6 by lpx_sn_deliftable_dropable, cpx_inv_lift1/ qed-.
-
-lemma drop_lpx_trans: ∀h,o,G. dedropable_sn (lpx h o G).
-/3 width=10 by lpx_sn_liftable_dedropable, cpx_lift/ qed-.
-
-lemma lpx_drop_trans_O1: ∀h,o,G. dropable_dx (lpx h o G).
-/2 width=3 by lpx_sn_dropable/ qed-.
-
-(* Properties on supclosure *************************************************)
-
-lemma fqu_lpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                     ∀K2. ⦃G2, L2⦄ ⊢ ➡[h, o] K2 →
-                     ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h, o] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h, o] T & ⦃G1, K1, T⦄ ⊐ ⦃G2, K2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_flat_dx, lpx_pair, ex3_2_intro/
-[ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpx_inv_pair1 … H) -H
-  #K2 #W2 #HLK2 #HVW2 #H destruct
-  /3 width=5 by cpx_pair_sn, fqu_bind_dx, ex3_2_intro/
-| #G #L1 #K1 #T1 #U1 #k #HLK1 #HTU1 #K2 #HK12
-  elim (drop_lpx_trans … HLK1 … HK12) -HK12
-  /3 width=7 by fqu_drop, ex3_2_intro/
-]
-qed-.
-
-lemma fquq_lpx_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                      ∀K2. ⦃G2, L2⦄ ⊢ ➡[h, o] K2 →
-                      ∃∃K1,T. ⦃G1, L1⦄ ⊢ ➡[h, o] K1 & ⦃G1, L1⦄ ⊢ T1 ➡[h, o] T & ⦃G1, K1, T⦄ ⊐⸮ ⦃G2, K2, T2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #K2 #HLK2 elim (fquq_inv_gen … H) -H
-[ #HT12 elim (fqu_lpx_trans … HT12 … HLK2) /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-lemma lpx_fqu_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                     ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 →
-                     ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[h, o] T & ⦃G1, K1, T⦄ ⊐ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=7 by fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpx_pair, ex3_2_intro/
-[ #I #G1 #L1 #V1 #X #H elim (lpx_inv_pair2 … H) -H
-  #K1 #W1 #HKL1 #HWV1 #H destruct elim (lift_total V1 0 1)
-  /4 width=7 by cpx_delta, fqu_drop, drop_drop, ex3_2_intro/
-| #G #L1 #K1 #T1 #U1 #k #HLK1 #HTU1 #L0 #HL01
-  elim (lpx_drop_trans_O1 … HL01 … HLK1) -L1
-  /3 width=5 by fqu_drop, ex3_2_intro/
-]
-qed-.
-
-lemma lpx_fquq_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                      ∀K1. ⦃G1, K1⦄ ⊢ ➡[h, o] L1 →
-                      ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ➡[h, o] T & ⦃G1, K1, T⦄ ⊐⸮ ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ➡[h, o] L2.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 elim (fquq_inv_gen … H) -H
-[ #HT12 elim (lpx_fqu_trans … HT12 … HKL1) /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
-]
-qed-.