milestone update in ground_2 and basic_2A

[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
deleted file mode 100644 (file)
index 270e8dc..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_fpcs.etc
+++ /dev/null
@@ -1,66 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 *)