matita/matita/contribs/lambdadelta/static_2/etc/teqx/feqx_fqus.etc

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  14
  15 include "static_2/static/reqx_fqus.ma".
  16 include "static_2/static/feqx.ma".
  17
  18 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
  19
  20 (* Properties with star-iterated structural successor for closures **********)
  21
  22 lemma feqx_fqus_trans (b):
  23       ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ →
  24       ∀G2,L2,T2. ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ →
  25       ∃∃G,L0,T0. ❪G1,L1,T1❫ ⬂*[b] ❪G,L0,T0❫ & ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫.
  26 #b #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
  27 elim(feqx_inv_gen_dx … H1) -H1 #HG #HL1 #HT1 destruct
  28 elim (reqx_fqus_trans … H2 … HL1) -L #L #T0 #H2 #HT02 #HL2
  29 elim (teqx_fqus_trans … H2 … HT1) -T #L0 #T #H2 #HT0 #HL0
  30 lapply (teqx_reqx_conf_sn … HT02 … HL0) -HL0 #HL0
  31 /4 width=7 by feqx_intro_dx, reqx_trans, teqx_trans, ex2_3_intro/
  32 qed-.