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15 include "basic_2/grammar/fsups.ma".
16 include "basic_2/substitution/ldrop_fsup.ma".
18 (* LOCAL ENVIRONMENT SLICING ************************************************)
20 (* Inversion lemmas on plus-iterated supclosure ****************************)
22 lemma fsupp_inv_atom1_fsups: ∀J,L1,L2,T2. ⦃L1, ⓪{J}⦄ ⊃+ ⦃L2, T2⦄ →
23 ∃∃I,K,V,i. ⇩[0, i] L1 ≡ K.ⓑ{I}V &
24 ⦃K, V⦄ ⊃* ⦃L2, T2⦄ & J = LRef i.
25 #J #L1 #L2 #T2 #H @(fsupp_ind … H) -L2 -T2
27 elim (fsup_inv_atom1_ldrop … H) -H * #i #HL12 #H destruct /2 width=7/
28 | #L #T #L2 #T2 #_ #HT2 * #I #K #V #i #HLK #HVT #H destruct /3 width=8/