matita/matita/contribs/lambdadelta/static_2/static/feqx_feqx.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/feqg_feqg.ma".
  16 include "static_2/static/feqx.ma".
  17
  18 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma feqx_dec (G1) (G2) (L1) (L2) (T1) (T2):
  23       Decidable (❨G1,L1,T1❩ ≅ ❨G2,L2,T2❩).
  24 /3 width=1 by feqg_dec, sfull_dec/ qed-.
  25 (*
  26 lemma feqx_sym: tri_symmetric … feqx.
  27 #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -L1 -T1
  28 /3 width=1 by feqx_intro_dx, reqx_sym, teqx_sym/
  29 qed-.
  30
  31 (* Main properties **********************************************************)
  32
  33 theorem feqx_trans: tri_transitive … feqx.
  34 #G1 #G #L1 #L #T1 #T * -G -L -T
  35 #L #T #HL1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
  36 /4 width=5 by feqx_intro_sn, reqx_trans, teqx_reqx_div, teqx_trans/
  37 qed-.
  38
  39 theorem feqx_canc_sn: ∀G,G1,L,L1,T,T1. ❨G,L,T❩ ≛ ❨G1,L1,T1❩→
  40                       ∀G2,L2,T2. ❨G,L,T❩ ≛ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩.
  41 /3 width=5 by feqx_trans, feqx_sym/ qed-.
  42
  43 theorem feqx_canc_dx: ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≛ ❨G,L,T❩ →
  44                       ∀G2,L2,T2. ❨G2,L2,T2❩ ≛ ❨G,L,T❩ → ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩.
  45 /3 width=5 by feqx_trans, feqx_sym/ qed-.
  46
  47 (* Main inversion lemmas with degree-based equivalence on terms *************)
  48
  49 theorem feqx_tneqx_repl_dx: ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ≛ ❨G2,L2,T2❩ →
  50                             ∀U1,U2. ❨G1,L1,U1❩ ≛ ❨G2,L2,U2❩ →
  51                             (T2 ≛ U2 → ⊥) → (T1 ≛ U1 → ⊥).
  52 #G1 #G2 #L1 #L2 #T1 #T2 #HT #U1 #U2 #HU #HnTU2 #HTU1
  53 elim (feqx_inv_gen_sn … HT) -HT #_ #_ #HT
  54 elim (feqx_inv_gen_sn … HU) -HU #_ #_ #HU
  55 /3 width=5 by teqx_repl/
  56 qed-.
  57 *)