matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_llor.ma

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  14
  15 include "basic_2A/substitution/lpx_sn_alt.ma".
  16 include "basic_2A/multiple/llor.ma".
  17 include "basic_2A/multiple/lleq_alt.ma".
  18
  19 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
  20
  21 (* Inversion lemmas on pointwise union for local environments ****************)
  22
  23 lemma llpx_sn_llor_fwd_sn: ∀R. (∀L. reflexive … (R L)) →
  24                            ∀L1,L2,T,l. llpx_sn R l T L1 L2 →
  25                            ∀L. L1 ⋓[T, l] L2 ≡ L → lpx_sn R L1 L.
  26 #R #HR #L1 #L2 #T #l #H1 #L #H2
  27 elim (llpx_sn_llpx_sn_alt … H1) -H1 #HL12 #IH1
  28 elim H2 -H2 #_ #HL1 #IH2
  29 @lpx_sn_intro_alt // #I1 #I #K1 #K #V1 #V #i #HLK1 #HLK
  30 lapply (drop_fwd_length_lt2 … HLK) #HiL
  31 elim (drop_O1_lt (Ⓕ) L2 i) // -HiL -HL1 -HL12 #I2 #K2 #V2 #HLK2
  32 elim (IH2 … HLK1 HLK2 HLK) -IH2 -HLK * /2 width=1 by conj/
  33 #HnT #H1 #H2 elim (IH1 … HnT … HLK1 HLK2) -IH1 -HnT -HLK1 -HLK2 /2 width=1 by conj/
  34 qed-.