matita/matita/contribs/lambdadelta/ground_2/lib/functions.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/lib/relations.ma".
  16
  17 (* FUNCTIONS ****************************************************************)
  18
  19 definition left_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f i a.
  20
  21 definition right_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f a i.
  22
  23 definition compatible_2 (A) (B): relation3 … (relation A) (relation B) ≝
  24                                  λf,Sa,Sb.
  25                                  ∀a1,a2. Sa a1 a2 → Sb (f a1) (f a2).
  26
  27 definition compatible_3 (A) (B) (C): relation4 … (relation A) (relation B) (relation C) ≝
  28                                      λf,Sa,Sb,Sc.
  29                                      ∀a1,a2. Sa a1 a2 → ∀b1,b2. Sb b1 b2 → Sc (f a1 b1) (f a2 b2).