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

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  14
  15 include "basic_2/static/frees_fqup.ma".
  16 include "basic_2/static/rex.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 rex_refl: ∀R. (∀L. reflexive … (R L)) → ∀L,T. L ⪤[R, T] L.
  24 #R #HR #L #T elim (frees_total L T)
  25 /4 width=3 by sex_refl, ext2_refl, ex2_intro/
  26 qed.
  27
  28 lemma rex_pair_refl: ∀R. (∀L. reflexive … (R L)) →
  29                      ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤[R, T] L.ⓑ{I}V2.
  30 #R #HR #L #V1 #V2 #HV12 #I #T
  31 elim (frees_total (L.ⓑ{I}V1) T) #f #Hf
  32 elim (pn_split f) * #g #H destruct
  33 /5 width=3 by sex_refl, sex_next, sex_push, ext2_refl, ext2_pair, ex2_intro/
  34 qed.
  35
  36 (* Advanced inversion lemmas ************************************************)
  37
  38 lemma rex_inv_bind_void: ∀R,p,I,L1,L2,V,T. L1 ⪤[R, ⓑ{p,I}V.T] L2 →
  39                          L1 ⪤[R, V] L2 ∧ L1.ⓧ ⪤[R, T] L2.ⓧ.
  40 #R #p #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_bind_void … Hf) -Hf
  41 /6 width=6 by sle_sex_trans, sex_inv_tl, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
  42 qed-.
  43
  44 (* Advanced forward lemmas **************************************************)
  45
  46 lemma rex_fwd_bind_dx_void: ∀R,p,I,L1,L2,V,T. L1 ⪤[R, ⓑ{p,I}V.T] L2 →
  47                             L1.ⓧ ⪤[R, T] L2.ⓧ.
  48 #R #p #I #L1 #L2 #V #T #H elim (rex_inv_bind_void … H) -H //
  49 qed-.