matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lpx_sn/llpx_sn_tc.etc

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  14
  15 include "basic_2/substitution/llpx_sn_ldrop.ma".
  16
  17 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
  18
  19 (* Properties about transitive closure **************************************)
  20
  21 lemma llpx_sn_TC_pair_dx: ∀R. (∀I,L. reflexive … (R I L)) →
  22                           ∀I,L,V1,V2,T. LTC … (R I) L V1 V2 →
  23                           LTC … (llpx_sn R 0) T (L.ⓑ{I}V1) (L.ⓑ{I}V2).
  24 #R #HR #I #L #V1 #V2 #T #H @(TC_star_ind … V2 H) -V2
  25 /4 width=9 by llpx_sn_bind_repl_O, llpx_sn_refl, step, inj/
  26 qed.