ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / exteq.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
new file mode 100644 (file)
index 0000000..81d324b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground/lib/exteq.ma
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/doteq_4.ma".
+include "ground/lib/relations.ma".
+
+(* EXTENSIONAL EQUIVALENCE **************************************************)
+
+definition exteq (A,B:Type[0]): relation (A → B) ≝
+                                λf1,f2. ∀a. f1 a = f2 a.
+
+interpretation "extensional equivalence"
+   'DotEq A B f1 f2 = (exteq A B f1 f2).
+
+(* Basic_properties *********************************************************)
+
+lemma exteq_refl (A) (B): reflexive … (exteq A B).
+// qed.
+
+lemma exteq_repl (A) (B): replace_2 … (exteq A B) (exteq A B) (exteq A B).
+// qed-.
+
+lemma exteq_sym (A) (B): symmetric … (exteq A B).
+/2 width=1 by exteq_repl/ qed-.
+
+lemma exteq_trans (A) (B): Transitive … (exteq A B).
+/2 width=1 by exteq_repl/ qed-.
+