matita/matita/contribs/lambdadelta/basic_2/static/freq_freq.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_lreq.ma".
  16 include "basic_2/relocation/frees_frees.ma".
  17 include "basic_2/relocation/freq.ma".
  18
  19 (* RANGED EQUIVALENCE FOR CLOSURES  *****************************************)
  20
  21 (* Main properties **********************************************************)
  22
  23 theorem freq_trans: tri_transitive … freq.
  24 #G1 #G #L1 #L #T1 #T * -G -L -T
  25 #L #f1 #H1T11 #Hf1 #G2 #L2 #T2 * -G2 -L2 -T2 #L2 #f2 #HT12 #Hf2
  26 lapply (frees_lreq_conf … H1T11 … Hf1) #HT11
  27 lapply (frees_mono … HT12 … HT11) -HT11 -HT12
  28 /4 width=7 by fleq_intro, lreq_eq_repl_back, lreq_trans/
  29 qed-.
  30
  31 theorem freq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2.
  32                       ⦃G, L, T⦄ ≡ ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≡ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄.
  33 /3 width=5 by freq_trans, freq_sym/ qed-.
  34
  35 theorem freq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T.
  36                       ⦃G1, L1, T1⦄ ≡ ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≡ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄.
  37 /3 width=5 by freq_trans, freq_sym/ qed-.