matita/matita/contribs/lambdadelta/static_2/static/rex_lex.ma

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  14
  15 include "static_2/relocation/lex.ma".
  16 include "static_2/static/rex_fsle.ma".
  17 include "static_2/static/req.ma".
  18
  19 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
  20
  21 (* Properties with generic extension of a context-sensitive relation ********)
  22
  23 lemma rex_lex: ∀R,L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R, T] L2.
  24 #R #L1 #L2 * #f #Hf #HL12 #T
  25 elim (frees_total L1 T) #g #Hg
  26 /4 width=5 by sex_sdj, sdj_isid_sn, ex2_intro/
  27 qed.
  28
  29 (* Inversion lemmas with generic extension of a context sensitive relation **)
  30
  31 lemma rex_inv_lex_req: ∀R. c_reflexive … R →
  32                        rex_fsge_compatible R →
  33                        ∀L1,L2,T. L1 ⪤[R, T] L2 →
  34                        ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
  35 #R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
  36 elim (sex_sdj_split … ceq_ext … HL 𝐈𝐝 ?) -HL
  37 [ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ] -H1R
  38 lapply (sex_sdj … HL10 f1 ?) /2 width=1 by sdj_isid_sn/ #H
  39 elim (frees_sex_conf … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
  40 /4 width=7 by sle_sex_trans, (* 2x *) ex2_intro/
  41 qed-.