ground_2 released and permanently renamed as ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/functions.ma b/matita/matita/contribs/lambdadelta/ground/lib/functions.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/lib/relations.ma".
+
+(* FUNCTIONS ****************************************************************)
+
+definition left_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f i a.
+
+definition right_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f a i.
+
+definition compatible_2 (A) (B):
+                        relation3 … (relation A) (relation B) ≝
+                        λf,Sa,Sb.
+                        ∀a1,a2. Sa a1 a2 → Sb (f a1) (f a2).
+
+definition compatible_3 (A) (B) (C):
+                        relation4 … (relation A) (relation B) (relation C) ≝
+                        λf,Sa,Sb,Sc.
+                        ∀a1,a2. Sa a1 a2 → ∀b1,b2. Sb b1 b2 → Sc (f a1 b1) (f a2 b2).
+
+definition annulment_2 (A) (f): predicate A ≝
+                       λi:A. ∀a1,a2. i = f a1 a2 → ∧∧ i = a1 & i = a2.