matita/matita/contribs/lambdadelta/static_2/static/frees_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 "static_2/static/frees.ma".
  16
  17 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  18
  19 (* Main inversion lemmas ****************************************************)
  20
  21 theorem frees_mono: ∀f1,L,T. L ⊢ 𝐅+❨T❩ ≘ f1 → ∀f2. L ⊢ 𝐅+❨T❩ ≘ f2 → f1 ≡ f2.
  22 #f1 #L #T #H elim H -f1 -L -T
  23 [ /3 width=3 by frees_inv_sort, pr_isi_inv_eq_repl/
  24 | #f1 #i #Hf1 #g2 #H
  25   elim (frees_inv_atom … H) -H #f2 #Hf2 #H destruct
  26   /4 width=5 by pr_isi_inv_eq_repl, pr_pushs_eq_repl, pr_eq_next/
  27 | #f1 #I #L #V #_ #IH #g2 #H elim (frees_inv_pair … H) -H
  28   #f2 #Hf2 #H destruct /3 width=5 by pr_eq_next/
  29 | #f1 #I #L #Hf1 #g2 #H elim (frees_inv_unit … H) -H
  30   #f2 #Hf2 #H destruct /3 width=5 by pr_isi_inv_eq_repl, pr_eq_next/
  31 | #f1 #I #L #i #_ #IH #g2 #H elim (frees_inv_lref … H) -H
  32   #f2 #Hf2 #H destruct /3 width=5 by pr_eq_push/
  33 | /3 width=3 by frees_inv_gref, pr_isi_inv_eq_repl/
  34 | #f1V #f1T #f1 #p #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_bind … H) -H
  35   #f2V #f2T #HV #HT #Hf2 @(pr_sor_mono … Hf1) -Hf1
  36   /5 width=3 by pr_sor_eq_repl_fwd_dx, pr_sor_eq_repl_fwd_sn, pr_tl_eq_repl/ (**) (* full auto too slow *)
  37 | #f1V #f1T #f1 #I #L #V #T #_ #_ #Hf1 #IHV #IHT #f2 #H elim (frees_inv_flat … H) -H
  38   #f2V #f2T #HV #HT #Hf2 @(pr_sor_mono … Hf1) -Hf1
  39   /4 width=3 by pr_sor_eq_repl_fwd_dx, pr_sor_eq_repl_fwd_sn/ (**) (* full auto too slow *)
  40 ]
  41 qed-.