matita/matita/contribs/lambdadelta/static_2/static/fdeq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/notation/relations/stareqsn_8.ma".
  16 include "static_2/syntax/genv.ma".
  17 include "static_2/static/rdeq.ma".
  18
  19 (* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
  20
  21 inductive fdeq (h) (o) (G) (L1) (T1): relation3 genv lenv term ≝
  22 | fdeq_intro_sn: ∀L2,T2. L1 ≛[h, o, T1] L2 → T1 ≛[h, o] T2 →
  23                  fdeq h o G L1 T1 G L2 T2
  24 .
  25
  26 interpretation
  27    "degree-based equivalence on referred entries (closure)"
  28    'StarEqSn h o G1 L1 T1 G2 L2 T2 = (fdeq h o G1 L1 T1 G2 L2 T2).
  29
  30 (* Basic_properties *********************************************************)
  31
  32 lemma fdeq_intro_dx (h) (o) (G): ∀L1,L2,T2. L1 ≛[h, o, T2] L2 →
  33                                  ∀T1. T1 ≛[h, o] T2 → ⦃G, L1, T1⦄ ≛[h, o] ⦃G, L2, T2⦄.
  34 /3 width=3 by fdeq_intro_sn, tdeq_rdeq_div/ qed.
  35
  36 (* Basic inversion lemmas ***************************************************)
  37
  38 lemma fdeq_inv_gen_sn: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
  39                        ∧∧ G1 = G2 & L1 ≛[h, o, T1] L2 & T1 ≛[h, o] T2.
  40 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
  41 qed-.
  42
  43 lemma fdeq_inv_gen_dx: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ →
  44                        ∧∧ G1 = G2 & L1 ≛[h, o, T2] L2 & T1 ≛[h, o] T2.
  45 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  46 /3 width=3 by tdeq_rdeq_conf, and3_intro/
  47 qed-.
  48
  49 (* Basic_2A1: removed theorems 6:
  50               fleq_refl fleq_sym fleq_inv_gen
  51               fleq_trans fleq_canc_sn fleq_canc_dx
  52 *)