matita/matita/contribs/lambdadelta/basic_2/static/lfxs_fqup.ma

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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/static/frees_fqup.ma".
  16 include "basic_2/static/lfxs.ma".
  17
  18 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 (* Basic_2A1: uses: llpx_sn_refl *)
  23 lemma lfxs_refl: ∀R. (∀L. reflexive … (R L)) → ∀L,T. L ⪤*[R, T] L.
  24 #R #HR #L #T elim (frees_total L T) /3 width=3 by lexs_refl, ex2_intro/
  25 qed.
  26
  27 lemma lfxs_pair: ∀R. (∀L. reflexive … (R L)) →
  28                  ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤*[R, T] L.ⓑ{I}V2.
  29 #R #HR #L #V1 #V2 #HV12 #I #T
  30 elim (frees_total (L.ⓑ{I}V1) T) #f #Hf
  31 elim (pn_split f) * #g #H destruct
  32 /4 width=3 by lexs_refl, lexs_next, lexs_push, ex2_intro/
  33 qed.