matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_frees.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/frees.ma".
  16 include "basic_2A/multiple/llpx_sn_alt_rec.ma".
  17
  18 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
  19
  20 (* Properties on context-sensitive free variables ***************************)
  21
  22 fact llpx_sn_frees_trans_aux: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
  23                               ∀L2,U,l,i. L2 ⊢ i ϵ 𝐅*[l]⦃U⦄ →
  24                               ∀L1. llpx_sn R l U L1 L2 → L1 ⊢ i ϵ 𝐅*[l]⦃U⦄.
  25 #R #H1R #H2R #L2 #U #l #i #H elim H -L2 -U -l -i /3 width=2 by frees_eq/
  26 #I2 #L2 #K2 #U #W2 #l #i #j #Hlj #Hji #HnU #HLK2 #_ #IHW2 #L1 #HL12
  27 elim (llpx_sn_inv_alt_r … HL12) -HL12 #HL12 #IH
  28 lapply (drop_fwd_length_lt2 … HLK2) #Hj
  29 elim (drop_O1_lt (Ⓕ) L1 j) // -Hj -HL12 #I1 #K1 #W1 #HLK1
  30 elim (IH … HnU HLK1 HLK2) // -IH -HLK2 /5 width=11 by frees_be/
  31 qed-.
  32
  33 lemma llpx_sn_frees_trans: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
  34                            ∀L1,L2,U,l. llpx_sn R l U L1 L2 →
  35                            ∀i. L2 ⊢ i ϵ 𝐅*[l]⦃U⦄ → L1 ⊢ i ϵ 𝐅*[l]⦃U⦄.
  36 /2 width=6 by llpx_sn_frees_trans_aux/ qed-.