matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_plus.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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 "ground_2/relocation/mr2.ma".
  16
  17 (* MULTIPLE RELOCATION WITH PAIRS *******************************************)
  18
  19 rec definition pluss (cs:mr2) (i:nat) on cs ≝ match cs with
  20 [ nil2         ⇒ ◊
  21 | cons2 l m cs ⇒ ❨l + i,m❩;pluss cs i
  22 ].
  23
  24 interpretation "plus (multiple relocation with pairs)"
  25    'plus x y = (pluss x y).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma pluss_SO2: ∀l,m,cs. (❨l,m❩;cs) + 1 = ❨↑l,m❩;cs + 1.
  30 normalize // qed.
  31
  32 (* Basic inversion lemmas ***************************************************)
  33
  34 lemma pluss_inv_nil2: ∀i,cs. cs + i = ◊ → cs = ◊.
  35 #i * // normalize
  36 #l #m #cs #H destruct
  37 qed.
  38
  39 lemma pluss_inv_cons2: ∀i,l,m,cs2,cs. cs + i = ❨l,m❩;cs2 →
  40                        ∃∃cs1. cs1 + i = cs2 & cs = ❨l - i,m❩;cs1.
  41 #i #l #m #cs2 *
  42 [ normalize #H destruct
  43 | #l1 #m1 #cs1 whd in ⊢ (??%?→?); #H destruct
  44   <minus_plus_m_m /2 width=3 by ex2_intro/
  45 ]
  46 qed-.