- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / llpx / llpx_lleq.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llpx_lleq.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llpx_lleq.etc
new file mode 100644 (file)
index 0000000..e936cc5
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/llpx_lleq.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/reduction/cpx_lleq.ma".
+include "basic_2/reduction/llpx.ma".
+
+(* LAZY SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ***************)
+
+(* Properties on lazy equivalence for local environments ********************)
+
+lemma llpx_lrefl: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2.
+/2 width=1 by llpx_sn_lrefl/ qed-.
+
+lemma lleq_llpx_trans: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
+                       ∀L.⦃G, L2⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L.
+/3 width=3 by lleq_cpx_trans, lleq_llpx_sn_trans/ qed-.
+
+lemma lleq_llpx_conf: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
+                      ∀L.⦃G, L1⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L2⦄ ⊢ ➡[h, g, T, d] L.
+/3 width=3 by lleq_cpx_trans, lleq_llpx_sn_conf/ qed-.