matita/matita/contribs/lambdadelta/basic_2/etc_2A1/nta/lsubn_ldrop.etc

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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/dynamic/lsubn.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
  18
  19 (* Properties concerning basic local environment slicing ********************)
  20
  21 (* Note: the constant 0 cannot be generalized *)
  22 lemma lsubn_ldrop_O1_conf: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K1,e. ⇩[0, e] L1 ≡ K1 →
  23                            ∃∃K2. h ⊢ K1 :⊑ K2 & ⇩[0, e] L2 ≡ K2.
  24 #h #L1 #L2 #H elim H -L1 -L2
  25 [ /2 width=3/
  26 | #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
  27   elim (ldrop_inv_O1 … H) -H * #He #HLK1
  28   [ destruct
  29     elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
  30     <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
  31   | elim (IHL12 … HLK1) -L1 /3 width=3/
  32   ]
  33 | #L1 #L2 #V #W #H1VW #H2VW #_ #IHL12 #K1 #e #H
  34   elim (ldrop_inv_O1 … H) -H * #He #HLK1
  35   [ destruct
  36     elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
  37     <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
  38   | elim (IHL12 … HLK1) -L1 /3 width=3/
  39   ]
  40 ]
  41 qed.
  42
  43 (* Note: the constant 0 cannot be generalized *)
  44 (* Basic_1: was only: csubt_drop_abbr csubt_drop_abst *)
  45 lemma lsubn_ldrop_O1_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
  46                             ∃∃K1. h ⊢ K1 :⊑ K2 & ⇩[0, e] L1 ≡ K1.
  47 #h #L1 #L2 #H elim H -L1 -L2
  48 [ /2 width=3/
  49 | #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
  50   elim (ldrop_inv_O1 … H) -H * #He #HLK2
  51   [ destruct
  52     elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
  53     <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
  54   | elim (IHL12 … HLK2) -L2 /3 width=3/
  55   ]
  56 | #L1 #L2 #V #W #H1VW #H2VW #_ #IHL12 #K2 #e #H
  57   elim (ldrop_inv_O1 … H) -H * #He #HLK2
  58   [ destruct
  59     elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
  60     <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
  61   | elim (IHL12 … HLK2) -L2 /3 width=3/
  62   ]
  63 ]
  64 qed.