milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / fpa / fpas_fpas.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpa/fpas_fpas.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpa/fpas_fpas.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpa/fpas_fpas.etc
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fpa_fpa.ma".
+include "basic_2/multiple/fpas.ma".
+
+(* MULTIPLE AJUSTMENT *******************************************************)
+
+(* Advanced properties ******************************************************)
+
+lemma fpas_strip: ∀L0,L1,L2,T0,T1,T2,s. ⦃L0, T0⦄ ⇳[s] ⦃L1, T1⦄ → ⦃L0, T0⦄ ⇳*[s] ⦃L2, T2⦄ →
+                  ∃∃L,T. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ & ⦃L2, T2⦄ ⇳[s] ⦃L, T⦄.
+/3 width=4 by fpa_conf, bi_TC_strip/ qed-.
+
+(* Main properties **********************************************************)
+
+theorem fpas_conf: ∀s. bi_confluent … (fpas s).
+/3 width=4 by fpa_conf, bi_TC_confluent/ qed-.
+
+theorem fpas_trans: ∀s. bi_transitive … (fpas s).
+/2 width=4 by bi_TC_transitive/ qed-.
+
+theorem fpas_canc_sn: ∀L,L1,L2,T,T1,T2,s.
+                      ⦃L, T⦄ ⇳*[s] ⦃L1, T1⦄→ ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
+/3 width=4 by fpas_trans, fpas_sym/ qed-.
+
+theorem fpas_canc_dx: ∀L1,L2,L,T1,T2,T,s.
+                      ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L2, T2⦄ ⇳*[s] ⦃L, T⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
+/3 width=4 by fpas_trans, fpas_sym/ qed-.