- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cny / lpx_cpye.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/lpx_cpye.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/lpx_cpye.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/substitution/cpye_cpye.ma".
+include "basic_2/reduction/lpx_cpys.ma".
+
+axiom cpx_cpys_conf_lpx: ∀h,g,G,d,e.
+                         ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡[h, g] T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡[h, g] L1 →
+                         ∀T2. ⦃G, L0⦄ ⊢ T0 ▶*[d, e] T2 →
+                         ∃∃T. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] T & ⦃G, L0⦄ ⊢ T2 ➡[h, g] T.
+
+(* SN EXTENDED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *********************)
+
+(* Forward lemmas on evaluation for extended substitution *******************)
+
+lemma cpx_cpys_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
+                             ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+                             ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] U1 →
+                             ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
+                             ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
+#h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e #HTU1
+elim (cpx_cpys_conf_lpx … HT12 … HL12 … HTU1) -T1
+/3 width=9 by cpx_cpys_trans_lpx, cpye_cpys_conf/
+qed-.
+
+lemma cpx_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
+                        ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+                        ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] 𝐍⦃U1⦄ →
+                        ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
+                        ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
+#h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e *
+/2 width=9 by cpx_cpys_cpye_fwd_lpx/
+qed-.