matita/matita/contribs/lambdadelta/static_2/syntax/teq_ext.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/notation/relations/ideq_3.ma".
  16 include "static_2/syntax/teqg_ext.ma".
  17 include "static_2/syntax/teq.ma".
  18
  19 (* SYNTACTIC EQUIVALENCE ****************************************************)
  20
  21 definition ceq: relation3 lenv term term ≝
  22            ceqg (pr_eq …).
  23
  24 definition ceq_ext: lenv → relation bind ≝
  25            ceqg_ext (pr_eq …).
  26
  27 interpretation
  28   "context-dependent syntactic equivalence (term)"
  29   'IdEq L T1 T2 = (ceq L T1 T2).
  30
  31 interpretation
  32   "context-dependent syntactic equivalence (binder)"
  33   'IdEq L I1 I2 = (ceq_ext L I1 I2).
  34
  35 (* Basic properties *********************************************************)
  36
  37 lemma ceq_ext_refl (L):
  38      reflexive … (ceq_ext L).
  39 /2 width=1 by ext2_refl/ qed.
  40
  41 lemma ceq_ext_sym (L):
  42       symmetric … (ceq_ext L).
  43 #L @ext2_sym (**) (* full auto does not work *)
  44 /2 width=1 by teq_sym/
  45 qed-.
  46
  47 (* Basic inversion lemmas ***************************************************)
  48
  49 lemma ceq_ext_inv_eq (L):
  50       ∀I1,I2. L ⊢ I1 ≡ I2 → I1 = I2.
  51 #L #I1 #I2 * -I1 -I2
  52 /3 width=4 by teq_inv_eq, eq_f3/
  53 qed-.