matita/matita/contribs/lambdadelta/basic_2/etc/lpx_sn/lleq_llor.etc

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  14
  15 include "basic_2/relocation/llor.ma".
  16 include "basic_2/substitution/lleq_alt.ma".
  17
  18 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
  19
  20 (* Properties on poinwise union for local environments **********************)
  21
  22 lemma llor_lleq_O: ∀T,L1,L2,L. L1 ⩖[T] L2 ≡ L → |L1| ≤ |L2| → |L2| = |L| → L2 ⋕[T, yinj 0] L.
  23 #T #L1 @(f2_ind … rfw … L1 T) -L1 -T
  24 #n #IH #L1 #T #Hn #L2 #L #H #HL12 #HL2 elim (llor_inv_alt … H) // destruct
  25 #HL1 #IHT @lleq_intro_alt //
  26 #I2 #I #K2 #K #V2 #V #i #_ #HnT #HLK2 #HLK lapply (ldrop_fwd_length_lt2 … HLK)
  27 #Hi elim (ldrop_O1_lt L1 i) //
  28 #I1 #K1 #V1 #HLK1 elim (IHT … HLK1 HLK) >HL1 >HL2 <minus_n_n -IHT -HLK1 -HLK
  29 [
  30 | * #I0 #K0 #V0 #_ #HLK0 lapply (ldrop_mono … HLK0 … HLK2) -HLK0 -HLK2
  31   #H1 #H2 #H3 #_ destruct
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