matita/matita/contribs/lambdadelta/basic_2/static/lfeq_lreq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   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/static/frees_lreq.ma".
  16 include "basic_2/static/lfeq.ma".
  17
  18 (* EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *******************)
  19
  20 (* Inversion lemmas with ranged equivalence for local environments **********)
  21
  22 lemma lfeq_inv_lreq: ∀L1,L2,T. L1 ≡[T] L2 → ∃∃f. L1 ⊢ 𝐅*⦃T⦄ ≡ f & L1 ≡[f] L2.
  23 #L1 #L2 #T * /2 width=3 by ex2_intro/
  24 qed-.
  25
  26 (* Properties with ranged equivalence for local environments ****************)
  27
  28 lemma lreq_lfeq: ∀L1,L2,T,f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ≡[f] L2 → L1 ≡[T] L2.
  29 /2 width=3 by ex2_intro/ qed.
  30
  31 (* Advanced properties ******************************************************)
  32
  33 lemma lfeq_sym: ∀T. symmetric … (lfeq T).
  34 #T #L1 #L2 #H elim (lfeq_inv_lreq … H) -H
  35 /3 width=3 by lreq_lfeq, frees_lreq_conf, lreq_sym/
  36 qed-.