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4 (* ||A|| A project by Andrea Asperti *)
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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 }.
19 include "basic_2/unfold/ltpss_sn.ma".
21 (* BASIC LOCAL ENVIRONMENT THINNING *****************************************)
23 definition thin: nat → nat → relation lenv ≝
24 λd,e,L1,L2. ∃∃L. L1 ⊢ ▶* [d, e] L & ⇩[d, e] L ≡ L2.
26 interpretation "basic thinning (local environment)"
27 'TSubst L1 d e L2 = (thin d e L1 L2).
29 (* Basic properties *********************************************************)
31 lemma ldrop_thin: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ▼*[d, e] L1 ≡ L2.
34 (* Basic inversion lemmas ***************************************************)
36 lemma thin_inv_thin1: ∀I,K1,V1,L2,e. ▼*[0, e] K1.ⓑ{I} V1 ≡ L2 → 0 < e →
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/