matita/matita/contribs/lambdadelta/ground/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/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):
  24                         relation3 … (relation A) (relation B) ≝
  25                         λf,Sa,Sb.
  26                         ∀a1,a2. Sa a1 a2 → Sb (f a1) (f a2).
  27
  28 definition compatible_3 (A) (B) (C):
  29                         relation4 … (relation A) (relation B) (relation C) ≝
  30                         λf,Sa,Sb,Sc.
  31                         ∀a1,a2. Sa a1 a2 → ∀b1,b2. Sb b1 b2 → Sc (f a1 b1) (f a2 b2).
  32
  33 definition annulment_2 (A) (f): predicate A ≝
  34                        λi:A. ∀a1,a2. i = f a1 a2 → ∧∧ i = a1 & i = a2.