- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpr / fpcs_fpcs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_fpcs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_fpcs.etc
new file mode 100644 (file)
index 0000000..270e8dc
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_fpcs.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/computation/fprs_fprs.ma".
+include "basic_2/conversion/fpc_fpc.ma".
+include "basic_2/equivalence/fpcs_fprs.ma".
+
+(* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma fpcs_inv_fprs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ →
+                     ∃∃L,T. ⦃L1, T1⦄ ➡* ⦃L, T⦄ & ⦃L2, T2⦄ ➡* ⦃L, T⦄.
+#L1 #L2 #T1 #T2 #H @(fpcs_ind … H) -L2 -T2
+[ /3 width=4/
+| #L #L2 #T #T2 #_ #HT2 * #L0 #T0 #HT10 elim HT2 -HT2 #HT2 #HT0
+  [ elim (fprs_strip … HT2 … HT0) -L -T #L #T #HT2 #HT0
+    lapply (fprs_strap1 … HT10 … HT0) -L0 -T0 /2 width=4/
+  | lapply (fprs_strap2 … HT2 … HT0) -L -T /2 width=4/
+  ]
+]
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma fpr_fprs_conf: ∀L,L1,L2,T,T1,T2. ⦃L, T⦄ ➡* ⦃L1, T1⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
+#L #L1 #L2 #T #T1 #T2 #HT1 #HT2
+elim (fprs_strip … HT2 … HT1) /2 width=4 by fpr_fprs_div/
+qed-.
+
+lemma fprs_fpr_conf: ∀L,L1,L2,T,T1,T2. ⦃L, T⦄ ➡* ⦃L1, T1⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → ⦃L2, T2⦄ ⬌* ⦃L1, T1⦄.
+#L #L1 #L2 #T #T1 #T2 #HT1 #HT2
+elim (fprs_strip … HT2 … HT1) /2 width=4 by fprs_fpr_div/
+qed-.
+
+lemma fprs_conf: ∀L,L1,L2,T,T1,T2. ⦃L, T⦄ ➡* ⦃L1, T1⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
+#L #L1 #L2 #T #T1 #T2 #HT1 #HT2
+elim (fprs_conf … HT1 … HT2) /2 width=4/
+qed-.
+
+lemma fpcs_strip: ∀L0,L1,T0,T1. ⦃L0, T0⦄ ⬌ ⦃L1, T1⦄ →
+                  ∀L2,T2. ⦃L0, T0⦄ ⬌* ⦃L2, T2⦄ →
+                  ∃∃L,T. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ & ⦃L2, T2⦄ ⬌ ⦃L, T⦄.
+/3 width=4/ qed.
+
+(* Main properties **********************************************************)
+
+theorem fpcs_trans: bi_transitive … fpcs.
+/2 width=4/ qed.
+
+theorem fpcs_canc_sn: ∀L,L1,L2,T,T1,T2. ⦃L, T⦄ ⬌* ⦃L1, T1⦄ → ⦃L, T⦄ ⬌* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
+/3 width=4 by fpcs_trans, fpcs_sym/ qed. (**) (* /3 width=3/ is too slow *)
+
+theorem fpcs_canc_dx: ∀L1,L2,L,T1,T2,T. ⦃L1, T1⦄ ⬌* ⦃L, T⦄ → ⦃L2, T2⦄ ⬌* ⦃L, T⦄ → ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄.
+/3 width=4 by fpcs_trans, fpcs_sym/ qed. (**) (* /3 width=3/ is too slow *)