matita/matita/contribs/lambdadelta/basic_2/relocation/lleq_leq.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/relocation/llpx_sn_leq.ma".
  16 include "basic_2/relocation/lleq.ma".
  17
  18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
  19
  20 (* Properties on equivalence for local environments *************************)
  21
  22 lemma leq_lleq_trans: ∀L2,L,T,d. L2 ⋕[T, d] L →
  23                       ∀L1. L1 ≃[d, ∞] L2 → L1 ⋕[T, d] L.
  24 /2 width=3 by leq_llpx_sn_trans/ qed-.
  25
  26 lemma lleq_leq_trans: ∀L,L1,T,d. L ⋕[T, d] L1 →
  27                       ∀L2. L1 ≃[d, ∞] L2 → L ⋕[T, d] L2.
  28 /2 width=3 by llpx_sn_leq_trans/ qed-.
  29
  30 lemma lleq_leq_repl: ∀L1,L2,T,d. L1 ⋕[T, d] L2 → ∀K1. K1 ≃[d, ∞] L1 →
  31                      ∀K2. L2 ≃[d, ∞] K2 → K1 ⋕[T, d] K2.
  32 /2 width=5 by llpx_sn_leq_repl/ qed-.