matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_cpcs.ma

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_equivalence/cpcs_cprs.ma".
  16 include "basic_2/i_dynamic/ntas.ma".
  17
  18 (* ITERATED NATIVE TYPE ASSIGNMENT FOR TERMS ********************************)
  19
  20 (* Properties with r-equivalence for terms **********************************)
  21
  22 lemma ntas_zero (h) (a) (G) (L):
  23       ∀T1,T2. ❪G,L❫ ⊢ T1 ![h,a] → ❪G,L❫ ⊢ T2 ![h,a] → ❪G,L❫ ⊢ T1 ⬌*[h] T2 → ❪G,L❫ ⊢ T1 :*[h,a,0] T2.
  24 #h #a #G #L #T1 #T2 #HT1 #HT2 #H
  25 elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
  26 /2 width=3 by ntas_intro/
  27 qed.
  28
  29 (* Inversion lemmas with r-equivalence for terms ****************************)
  30
  31 lemma ntas_inv_zero (h) (a) (G) (L):
  32       ∀T1,T2. ❪G,L❫ ⊢ T1 :*[h,a,0] T2 →
  33       ∧∧ ❪G,L❫ ⊢ T1 ![h,a] & ❪G,L❫ ⊢ T2 ![h,a] & ❪G,L❫ ⊢ T1 ⬌*[h] T2.
  34 #h #a #G #L #T1 #T2 * #T0 #HT1 #HT2 #HT20 #HT10
  35 /3 width=3 by cprs_div, and3_intro/
  36 qed-.