matita/matita/contribs/lambdadelta/ground/lib/lstar_2a.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/ltc.ma".
  16 include "ground/arith/nat_plus.ma".
  17
  18 (* NAT-LABELED REFLEXIVE AND TRANSITIVE CLOSURE FOR FOR λδ-2A ***************)
  19
  20 definition lstar_aux (B) (R:relation B) (l): relation B ≝
  21            λb1,b2. ∨∨ (∧∧ l = 𝟎 & b1 = b2) | (∧∧ l = 𝟏  & R b1 b2).
  22
  23 definition lstar (B) (R:relation B): nat → relation B ≝
  24            ltc … nplus … (lstar_aux … R).
  25
  26 definition llstar (A) (B) (R:relation3 A B B) (l:nat): relation3 A B B ≝
  27            λa. lstar … (R a) l.