milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / llpr / llpr_ldrop.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpr/llpr_ldrop.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpr/llpr_ldrop.etc
deleted file mode 100644 (file)
index 74f7cc6..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpr/llpr_ldrop.etc
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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/relocation/fquq_alt.ma".
-include "basic_2/static/ssta_llpx_sn.ma".
-include "basic_2/reduction/cpr_lift.ma".
-include "basic_2/reduction/cpr_llpx_sn.ma".
-include "basic_2/reduction/llpr.ma".
-
-(* LAZY SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ************************)
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma llpr_inv_lref_ge_dx: ∀G,L1,L2,d,i. ⦃G, L1⦄ ⊢ ➡[#i, d] L2 → d ≤ i →
-                           ∀I,K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 →
-                           ∃∃K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 &
-                                    ⦃G, K1⦄ ⊢ ➡[V1, 0] K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2.
-/2 width=5 by llpx_sn_inv_lref_ge_dx/ qed-.
-
-lemma llpr_inv_lref_ge_sn: ∀G,L1,L2,d,i. ⦃G, L1⦄ ⊢ ➡[#i, d] L2 → d ≤ i →
-                           ∀I,K1,V1. ⇩[i] L1 ≡ K1.ⓑ{I}V1 →
-                           ∃∃K2,V2. ⇩[i] L2 ≡ K2.ⓑ{I}V2 &
-                                    ⦃G, K1⦄ ⊢ ➡[V1, 0] K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2.
-/2 width=5 by llpx_sn_inv_lref_ge_sn/ qed-.
-
-lemma llpr_inv_lref_ge_bi: ∀G,L1,L2,d,i. ⦃G, L1⦄ ⊢ ➡[#i, d] L2 → d ≤ i →
-                           ∀I1,I2,K1,K2,V1,V2.
-                           ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
-                           ∧∧ I1 = I2 & ⦃G, K1⦄ ⊢ ➡[V1, 0] K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2.
-/2 width=8 by llpx_sn_inv_lref_ge_bi/ qed-.
-
-lemma llpr_inv_bind_O: ∀a,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡ [ⓑ{a,I}V.T, 0] L2 →
-                       ⦃G, L1⦄ ⊢ ➡[V, 0] L2 ∧ ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡[T, 0] L2.ⓑ{I}V.
-/2 width=2 by llpx_sn_inv_bind_O/ qed-.
-
-lemma llpr_bind_repl_O: ∀I,G,L1,L2,V1,V2,T. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ➡[T, 0] L2.ⓑ{I}V2 →
-                        ∀J,W1,W2. ⦃G, L1⦄ ⊢ ➡[W1, 0] L2 → ⦃G, L1⦄ ⊢ W1 ➡ W2 → ⦃G, L1.ⓑ{J}W1⦄ ⊢ ➡[T, 0] L2.ⓑ{J}W2.
-/2 width=4 by llpx_sn_bind_repl_O/ qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma llpr_ssta_conf: ∀h,g,G. s_r_confluent1 … (ssta h g G) (llpr G 0).
-/3 width=10 by ssta_llpx_sn_conf, cpr_lift/ qed-.
-
-lemma llpr_cpr_conf: ∀G. s_r_confluent1 … (cpr G) (llpr G 0).
-/3 width=10 by cpr_llpx_sn_conf, cpr_inv_lift1, cpr_lift/ qed-.
-
-(* Properties on context-sensitive parallel reduction for terms *************)
-
-lemma fqu_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                        ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
-                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[T1, 0] L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃ ⦃G2, L2, U2⦄.
-#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=10 by llpr_lref, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ldrop_pair, ex3_2_intro/
-#G #L #K #U #T #e #HLK #HUT #U2 #HU2
-elim (lift_total U2 0 (e+1)) #T2 #HUT2
-lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
-qed-.
-
-lemma fquq_cpr_trans_dx: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
-                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[T1, 0] L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
-#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
-[ #HT12 elim (fqu_cpr_trans_dx … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-lemma fqu_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
-                        ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
-                        ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[T1, 0] L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃ ⦃G2, L2, U2⦄.
-#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-/3 width=10 by llpr_lref, cpr_pair_sn, cpr_bind, cpr_flat, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, ldrop_pair, ex3_2_intro/
-#G #L #K #U #T #e #HLK #HUT #U2 #HU2
-elim (lift_total U2 0 (e+1)) #T2 #HUT2
-lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
-qed-.
-
-lemma fquq_cpr_trans_sn: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                         ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡ U2 →
-                         ∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡[T1, 0] L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
-#G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 elim (fquq_inv_gen … H) -H
-[ #HT12 elim (fqu_cpr_trans_sn … HT12 … HTU2) /3 width=5 by fqu_fquq, ex3_2_intro/
-| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
-]
-qed-.