matita/matita/contribs/lambdadelta/basic_2/static/ffeq.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 "basic_2/notation/relations/lazyeq_6.ma".
  16 include "basic_2/static/lfeq_lreq.ma".
  17 include "basic_2/static/lfeq_fqup.ma".
  18
  19 (* EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *****************************)
  20
  21 inductive ffeq (G) (L1) (T): relation3 genv lenv term ≝
  22 | fleq_intro: ∀L2. L1 ≡[T] L2 → ffeq G L1 T G L2 T
  23 .
  24
  25 interpretation
  26    "equivalence on referred entries (closure)"
  27    'LazyEq G1 L1 T1 G2 L2 T2 = (ffeq G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma ffeq_refl: tri_reflexive … ffeq.
  32 /2 width=1 by fleq_intro/ qed.
  33
  34 lemma ffeq_sym: tri_symmetric … ffeq.
  35 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1 /3 width=1 by fleq_intro, lfeq_sym/
  36 qed-.
  37
  38 (* Basic inversion lemmas ***************************************************)
  39
  40 lemma ffeq_inv_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄ →
  41                     ∧∧ G1 = G2 & L1 ≡[T1] L2 & T1 = T2.
  42 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
  43 qed-.
  44
  45 (* Basic_2A1: removed theorems 6:
  46               fleq_refl fleq_sym fleq_inv_gen
  47               fleq_trans fleq_canc_sn fleq_canc_dx
  48 *)