matita/matita/contribs/lambdadelta/basic_2A/etc/delift/thin.etc

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  14
  15 notation "hvbox( ▼ * [ term 46 d , break term 46 e ] break term 46 T1 ≡ break term 46 T2 )"
  16    non associative with precedence 45
  17    for @{ 'TSubst $T1 $d $e $T2 }.
  18
  19 include "basic_2/unfold/ltpss_sn.ma".
  20
  21 (* BASIC LOCAL ENVIRONMENT THINNING *****************************************)
  22
  23 definition thin: nat → nat → relation lenv ≝
  24                  λd,e,L1,L2. ∃∃L. L1 ⊢ ▶* [d, e] L & ⇩[d, e] L ≡ L2.
  25
  26 interpretation "basic thinning (local environment)"
  27    'TSubst L1 d e L2 = (thin d e L1 L2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma ldrop_thin: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ▼*[d, e] L1 ≡ L2.
  32 /2 width=3/ qed.
  33
  34 (* Basic inversion lemmas ***************************************************)
  35
  36 lemma thin_inv_thin1: ∀I,K1,V1,L2,e. ▼*[0, e] K1.ⓑ{I} V1 ≡ L2 → 0 < e →
  37                       ▼*[0, e - 1] K1 ≡ L2.
  38 #I #K1 #V1 #L2 #e * #X #HK1 #HL2 #e
  39 elim (ltpss_sn_inv_tpss21 … HK1 ?) -HK1 // #K #V #HK1 #_ #H destruct
  40 lapply (ldrop_inv_ldrop1 … HL2 ?) -HL2 // /2 width=3/
  41 qed-.