matita/matita/contribs/lambdadelta/basic_2/syntax/cext2.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/syntax/ext2.ma".
  16 include "basic_2/syntax/lenv.ma".
  17
  18 (* EXTENSION TO BINDERS OF A CONTEXT-SENSITIVE RELATION FOR TERMS ***********)
  19
  20 definition cext2: (lenv → relation term) → lenv → relation bind ≝
  21                   λR,L. ext2 (R L).
  22
  23 (* Basic properties *********************************************************)
  24
  25 lemma cext2_sym: ∀R. (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
  26                  ∀L1,L2,I1,I2. cext2 R L1 I1 I2 → cext2 R L2 I2 I1.
  27 #R #HR #L1 #L2 #I1 #I2 * /3 width=2 by ext2_pair/
  28 qed-.
  29
  30 lemma cext2_co: ∀R1,R2. (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) →
  31                 ∀L,I1,I2. cext2 R1 L I1 I2 → cext2 R2 L I1 I2.
  32 #R1 #R2 #HR #L #I1 #I2 * /3 width=2 by ext2_unit, ext2_pair/
  33 qed-.