matita/matita/contribs/lambda_delta/basic_2/unfold/thin.ma

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  14
  15 include "basic_2/unfold/ltpss.ma".
  16
  17 (* LOCAL ENVIRONMENT THINNING ***********************************************)
  18
  19 definition thin: nat → nat → relation lenv ≝
  20                  λd,e,L1,L2. ∃∃L. L1 [d, e] ▶* L & ⇩[d, e] L ≡ L2.
  21
  22 interpretation "thinning (local environment)"
  23    'TSubst L1 d e L2 = (thin d e L1 L2).
  24
  25 (* Basic properties *********************************************************)
  26
  27 lemma ldrop_thin: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → L1 [d, e] ≡ L2.
  28 /2 width=3/ qed.
  29
  30 (* Basic inversion lemmas ***************************************************)
  31
  32 lemma thin_inv_thin1: ∀I,K1,V1,L2,e. K1. ⓑ{I} V1 [0, e] ≡ L2 → 0 < e →
  33                       K1 [0, e - 1] ≡ L2.
  34 #I #K1 #V1 #L2 #e * #X #HK1 #HL2 #e
  35 elim (ltpss_inv_tpss21 … HK1 ?) -HK1 // #K #V #HK1 #_ #H destruct
  36 lapply (ldrop_inv_ldrop1 … HL2 ?) -HL2 // /2 width=3/
  37 qed-.