matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubn/lsubn_cpcs.etc

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/equivalence/cpcs_cpcs.ma".
  16 include "basic_2/dynamic/lsubn.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
  19
  20 (* Properties on context-sensitive parallel equivalence for terms ***********)
  21
  22 (* Basic_1: was: csubt_pr2 *)
  23 lemma cpr_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
  24                        ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
  25 /3 width=4 by lsubn_fwd_lsubs2, cpr_lsubs_trans/ qed.
  26
  27 lemma cprs_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
  28                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
  29 /3 width=4 by lsubn_fwd_lsubs2, cprs_lsubs_trans/ qed.
  30
  31 (* Basic_1: was: csubt_pc3 *)
  32 lemma cpcs_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
  33                         ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
  34 /3 width=4 by lsubn_fwd_lsubs2, cpcs_lsubs_trans/ qed.