matita/matita/contribs/lambdadelta/basic_2/static/frees_lreq.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/lreq.ma".
  16 include "basic_2/static/frees.ma".
  17
  18 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  19
  20 (* Properties with ranged equivalence for local environments ****************)
  21
  22 lemma frees_lreq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f → ∀L2. L1 ≡[f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
  23 #f #L1 #T #H elim H -f -L1 -T
  24 [ #f #I #Hf #X #H lapply (lreq_inv_atom1 … H) -H
  25   #H destruct /2 width=1 by frees_atom/
  26 | #f #I #L1 #V1 #s #_ #IH #X #H elim (lreq_inv_push1 … H) -H
  27   /3 width=1 by frees_sort/
  28 | #f #I #L1 #V1 #_ #IH #X #H elim (lreq_inv_next1 … H) -H
  29   /3 width=1 by frees_zero/
  30 | #f #I #L1 #V1 #i #_ #IH #X #H elim (lreq_inv_push1 … H) -H
  31   /3 width=1 by frees_lref/
  32 | #f #I #L1 #V1 #l #_ #IH #X #H elim (lreq_inv_push1 … H) -H
  33   /3 width=1 by frees_gref/
  34 | /6 width=5 by frees_bind, lreq_inv_tl, sle_lreq_trans, sor_inv_sle_dx, sor_inv_sle_sn/
  35 | /5 width=5 by frees_flat, sle_lreq_trans, sor_inv_sle_dx, sor_inv_sle_sn/
  36 ]
  37 qed-.
  38
  39 lemma lreq_frees_trans: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f → ∀L2. L2 ≡[f] L1 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
  40 /3 width=3 by frees_lreq_conf, lreq_sym/ qed-.