update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / fleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq.ma
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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_2A/notation/relations/lazyeq_7.ma".
+include "basic_2A/grammar/genv.ma".
+include "basic_2A/multiple/lleq.ma".
+
+(* LAZY EQUIVALENCE FOR CLOSURES ********************************************)
+
+inductive fleq (l) (G) (L1) (T): relation3 genv lenv term ≝
+| fleq_intro: ∀L2. L1 ≡[T, l] L2 → fleq l G L1 T G L2 T
+.
+
+interpretation
+   "lazy equivalence (closure)"
+   'LazyEq l G1 L1 T1 G2 L2 T2 = (fleq l G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fleq_refl: ∀l. tri_reflexive … (fleq l).
+/2 width=1 by fleq_intro/ qed.
+
+lemma fleq_sym: ∀l. tri_symmetric … (fleq l).
+#l #G1 #L1 #T1 #G2 #L2 #T2 * /3 width=1 by fleq_intro, lleq_sym/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma fleq_inv_gen: ∀G1,G2,L1,L2,T1,T2,l. ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄ →
+                    ∧∧ G1 = G2 & L1 ≡[T1, l] L2 & T1 = T2.
+#G1 #G2 #L1 #L2 #T1 #T2 #l * -G2 -L2 -T2 /2 width=1 by and3_intro/
+qed-.