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15 include "basic_2/substitution/llneq_alt.ma".
17 (* NEGATED LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **************************)
19 (* Advanced inversion lemmas ************************************************)
21 lemma llneq_inv_atom1: ∀L1,L2,T,d. L1 ⧣⧣[T, d] L2 → |L1| ≤ d → ⊥.
22 #L1 #L2 #T #d #H elim H -L1 -L2 -T -d /2 width=1 by/
23 [ #I1 #I2 #L1 #L2 #K1 #K2 #V1 #V2 #d #i #Hdi #HLK1 #_ #_ #_
24 >(ldrop_fwd_length … HLK1) -HLK1 normalize
25 #H lapply (yle_trans … H … Hdi) -d
26 /3 width=4 by yle_inv_inj, le_plus_xySz_x_false/
27 | #I1 #I2 #L1 #L2 #K1 #K2 #V #d #i #Hdi #HLK1 #_ #_ #_
28 >(ldrop_fwd_length … HLK1) -HLK1 normalize
29 #H lapply (yle_trans … H … Hdi) -d
30 /3 width=4 by yle_inv_inj, le_plus_xySz_x_false/
31 | #a #I #L1 <yplus_inj /4 width=1 by yle_succ/