matita/matita/contribs/lambdadelta/basic_2/etc/nta/lsubn_nta.etc

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   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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  14
  15 include "basic_2/dynamic/nta_nta.ma".
  16 include "basic_2/dynamic/lsubn_ldrop.ma".
  17 include "basic_2/dynamic/lsubn_cpcs.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
  20
  21 (* Properties concerning atomic arity assignment ****************************)
  22
  23 (* Note: the corresponding confluence property does not hold *)
  24 (* Basic_1: was: csubt_ty3 *)
  25 lemma lsubn_nta_trans: ∀h,L2,T,U. ⦃h, L2⦄ ⊢ T : U → ∀L1. h ⊢ L1 :⊑ L2 →
  26                        ⦃h, L1⦄ ⊢ T : U.
  27 #h #L2 #T #U #H elim H -L2 -T -U
  28 [ //
  29 | #L2 #K2 #V2 #W2 #U2 #i #HLK2 #_ #WU2 #IHVW2 #L1 #HL12
  30   elim (lsubn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  31   elim (lsubn_inv_pair2 … H) -H * #K1
  32   [ #HK12 #H destruct /3 width=6/
  33   | #V1 #_ #_ #_ #_ #H destruct
  34   ]
  35 | #L2 #K2 #W2 #V2 #U2 #i #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
  36   elim (lsubn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  37   elim (lsubn_inv_pair2 … H) -H * #K1 [ | -IHWV2 ]
  38   [ #HK12 #H destruct /3 width=6/
  39   | #V1 #H1V1W2 #_ #_ #H #_ destruct /2 width=6/
  40   ]
  41 | /4 width=2/
  42 | /3 width=1/
  43 | /3 width=2/
  44 | /3 width=1/
  45 | /4 width=6/
  46 ]
  47 qed.