milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / llpx / llpxs_lleq.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llpxs_lleq.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llpxs_lleq.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/llpx/llpxs_lleq.etc
@@ -0,0 +1,66 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lleq_leq.ma".
+include "basic_2/reduction/llpx_lleq.ma".
+include "basic_2/computation/cpxs_lleq.ma".
+include "basic_2/computation/llpxs_cpxs.ma".
+
+(* LAZY SN EXTENDED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS *************)
+
+(* Properties on lazy equivalence for local environments ********************)
+
+lemma llpxs_lrefl: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, T, d] L2.
+/3 width=1 by llpx_lrefl, llpx_llpxs/ qed-.
+
+lemma lleq_llpxs_trans: ∀h,g,G,L2,L,T,d. ⦃G, L2⦄ ⊢ ➡*[h, g, T, d] L →
+                        ∀L1. L1 ⋕[T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, T, d] L.
+#h #g #G #L2 #L #T #d #H @(llpxs_ind … H) -L
+/3 width=3 by llpxs_strap1, llpxs_lrefl/
+qed-.
+
+lemma lleq_llpxs_conf: ∀h,g,G,L1,L,T,d. ⦃G, L1⦄ ⊢ ➡*[h, g, T, d] L →
+                       ∀L2. L1 ⋕[T, d] L2 → ⦃G, L2⦄ ⊢ ➡*[h, g, T, d] L.
+/3 width=3 by lleq_llpxs_trans, lleq_sym/ qed-.
+(*
+foct leq_lpxs_trans_lleq_aux: ∀h,g,G,L1,L0,d,e. L1 ≃[d, e] L0 → e = ∞ →
+                              ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
+                              ∃∃L. L ≃[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
+                                   (∀T. L0 ⋕[T, d] L2 ↔ L1 ⋕[T, d] L).
+#h #g #G #L1 #L0 #d #e #H elim H -L1 -L0 -d -e
+[ #d #e #_ #L2 #H >(lpxs_inv_atom1 … H) -H
+  /3 width=5 by ex3_intro, conj/
+| #I1 #I0 #L1 #L0 #V1 #V0 #_ #_ #He destruct
+| #I #L1 #L0 #V1 #e #HL10 #IHL10 #He #Y #H
+  elim (lpxs_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct
+  lapply (ysucc_inv_Y_dx … He) -He #He
+  elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH
+  @(ex3_intro … (L.ⓑ{I}V2)) /3 width=3 by lpxs_pair, leq_cpxs_trans, leq_pair/
+  #T elim (IH T) #HL0dx #HL0sn
+  @conj #H @(lleq_leq_repl … H) -H /3 width=1 by leq_sym, leq_pair_O_Y/
+| #I1 #I0 #L1 #L0 #V1 #V0 #d #e #HL10 #IHL10 #He #Y #H
+  elim (lpxs_inv_pair1 … H) -H #L2 #V2 #HL02 #HV02 #H destruct
+  elim (IHL10 … HL02) // -IHL10 -HL02 #L #HL2 #HL1 #IH
+  @(ex3_intro … (L.ⓑ{I1}V1)) /3 width=1 by lpxs_pair, leq_succ/
+  #T elim (IH T) #HL0dx #HL0sn
+  @conj #H @(lleq_leq_repl … H) -H /3 width=1 by leq_sym, leq_succ/
+]
+qed-.
+
+lamma leq_lpxs_trans_lleq: ∀h,g,G,L1,L0,d. L1 ≃[d, ∞] L0 →
+                           ∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
+                           ∃∃L. L ≃[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
+                                (∀T. L0 ⋕[T, d] L2 ↔ L1 ⋕[T, d] L).
+/2 width=1 by leq_lpxs_trans_lleq_aux/ qed-.
+*)