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

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  14
  15 include "basic_2/static/rdeq_fqus.ma".
  16 include "basic_2/static/fdeq.ma".
  17
  18 (* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
  19
  20 (* Properties with star-iterated structural successor for closures **********)
  21
  22 lemma fdeq_fqus_trans: ∀h,o,b,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ →
  23                        ∀G2,L2,T2. ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
  24                        ∃∃G,L0,T0. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L0, T0⦄ & ⦃G, L0, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
  25 #h #o #b #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
  26 elim(fdeq_inv_gen_dx … H1) -H1 #HG #HL1 #HT1 destruct
  27 elim (rdeq_fqus_trans … H2 … HL1) -L #L #T0 #H2 #HT02 #HL2
  28 elim (tdeq_fqus_trans … H2 … HT1) -T #L0 #T #H2 #HT0 #HL0
  29 lapply (tdeq_rdeq_conf … HT02 … HL0) -HL0 #HL0
  30 /4 width=7 by fdeq_intro_dx, rdeq_trans, tdeq_trans, ex2_3_intro/
  31 qed-.