matita/matita/contribs/lambdadelta/basic_2A/multiple/lleq_llor.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_2A/multiple/llor.ma".
  16 include "basic_2A/multiple/llpx_sn_frees.ma".
  17 include "basic_2A/multiple/lleq_alt.ma".
  18
  19 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
  20
  21 (* Properties on pointwise union for local environments **********************)
  22
  23 lemma llpx_sn_llor_dx: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
  24                        ∀L1,L2,T,l. llpx_sn R l T L1 L2 → ∀L. L1 ⋓[T, l] L2 ≡ L → L2 ≡[T, l] L.
  25 #R #H1R #H2R #L1 #L2 #T #l #H1 #L #H2
  26 lapply (llpx_sn_frees_trans … H1R H2R … H1) -H1R -H2R #HR
  27 elim (llpx_sn_llpx_sn_alt … H1) -H1 #HL12 #IH1
  28 elim H2 -H2 #_ #HL1 #IH2
  29 @lleq_intro_alt // #I2 #I #K2 #K #V2 #V #i #Hi #HnT #HLK2 #HLK
  30 lapply (drop_fwd_length_lt2 … HLK) #HiL
  31 elim (drop_O1_lt (Ⓕ) L1 i) // -HiL #I1 #K1 #V1 #HLK1
  32 elim (IH1 … HLK1 HLK2) -IH1 /2 width=1 by/ #H #_ destruct
  33 elim (IH2 … HLK1 HLK2 HLK) -IH2 -HLK1 -HLK2 -HLK * /2 width=1 by conj/ #H
  34 [ elim (ylt_yle_false … H) -H //
  35 | elim H -H /2 width=1 by/
  36 ]
  37 qed.
  38
  39 lemma llpx_sn_llor_dx_sym: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
  40                            ∀L1,L2,T,l. llpx_sn R l T L1 L2 → ∀L. L1 ⋓[T, l] L2 ≡ L → L ≡[T, l] L2.
  41 /3 width=6 by llpx_sn_llor_dx, lleq_sym/ qed.