update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / teq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/teq.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 "ground/notation/relations/ideq_2.ma".
+include "static_2/syntax/teqg.ma".
+
+(* SYNTACTIC EQUIVALENCE ON TERMS *******************************************)
+
+definition teq: relation term ≝
+           teqg (eq …).
+
+interpretation
+  "context-free syntactic equivalence (term)"
+  'IdEq T1 T2 = (teq T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma teq_refl:
+      reflexive … teq.
+/2 width=1 by teqg_refl/ qed.
+
+lemma teq_sym:
+      symmetric … teq.
+/2 width=1 by teqg_sym/ qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma teq_inv_eq:
+      ∀T1,T2. T1 ≡ T2 → T1 = T2.
+#T1 #T2 #H elim H -H //
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma teq_repl_1 (R:predicate …):
+      ∀T1. R T1 → ∀T2. T1 ≡ T2 → R T2.
+#R #T1 #HT1 #T2 #HT12
+<(teq_inv_eq … HT12) -T2 //
+qed-.
+
+lemma teq_sym_repl_1 (R:predicate …):
+      ∀T1. R T1 → ∀T2. T2 ≡ T1 → R T2.
+#R #T1 #HT1 #T2 #HT12
+>(teq_inv_eq … HT12) -T2 //
+qed-.