matita/matita/contribs/lambdadelta/basic_2A/etc/llneq/llneq_ext.etc

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  14
  15 include "basic_2/substitution/llneq_alt.ma".
  16
  17 (* NEGATED LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **************************)
  18
  19 (* Advanced inversion lemmas ************************************************)
  20
  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/
  32 ]
  33 qed-.