- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / lpc / lfpcs_lfpcs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpc/lfpcs_lfpcs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpc/lfpcs_lfpcs.etc
new file mode 100644 (file)
index 0000000..1e95217
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpc/lfpcs_lfpcs.etc
@@ -0,0 +1,50 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/computation/lfprs_lfprs.ma".
+include "basic_2/conversion/lfpc_lfpc.ma".
+include "basic_2/equivalence/lfpcs_lfprs.ma".
+
+(* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma lfpcs_inv_lfprs: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
+                       ∃∃L. ⦃L1⦄ ➡* ⦃L⦄ & ⦃L2⦄ ➡* ⦃L⦄.
+#L1 #L2 #H @(lfpcs_ind … H) -L2
+[ /3 width=3/
+| #L #L2 #_ #HL2 * #L0 #HL10 elim HL2 -HL2 #HL2 #HL0
+  [ elim (lfprs_strip … HL0 … HL2) -L #L #HL0 #HL2
+    lapply (lfprs_strap1 … HL10 … HL0) -L0 /2 width=3/
+  | lapply (lfprs_strap2 … HL2 … HL0) -L /2 width=3/
+  ]
+]
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma lfpcs_strip: ∀L,L1. ⦃L⦄ ⬌* ⦃L1⦄ → ∀L2. ⦃L⦄ ⬌ ⦃L2⦄ →
+                   ∃∃L0. ⦃L1⦄ ⬌ ⦃L0⦄ & ⦃L2⦄ ⬌* ⦃L0⦄.
+/3 width=3/ qed.
+
+(* Main properties **********************************************************)
+
+theorem lfpcs_trans: ∀L1,L. ⦃L1⦄ ⬌* ⦃L⦄ → ∀L2. ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/2 width=3/ qed.
+
+theorem lfpcs_canc_sn: ∀L,L1,L2. ⦃L⦄ ⬌* ⦃L1⦄ → ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3 by lfpcs_trans, lfpcs_sym/ qed.
+
+theorem lfpcs_canc_dx: ∀L,L1,L2. ⦃L1⦄ ⬌* ⦃L⦄ → ⦃L2⦄ ⬌* ⦃L⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
+/3 width=3 by lfpcs_trans, lfpcs_sym/ qed.