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15 include "static_2/static/reqg_fqus.ma".
16 include "static_2/static/feqg.ma".
18 (* GENERIC EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *********************)
20 (* Properties with star-iterated structural successor for closures **********)
22 lemma feqg_fqus_trans (S) (b):
23 reflexive … S → symmetric … S → Transitive … S →
24 ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →
25 ∀G2,L2,T2. ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ →
26 ∃∃G,L0,T0. ❪G1,L1,T1❫ ⬂*[b] ❪G,L0,T0❫ & ❪G,L0,T0❫ ≛[S] ❪G2,L2,T2❫.
27 #S #b #H1S #H2S #H3S #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
28 elim(feqg_inv_gen_dx … H1) -H1 // #HG #HL1 #HT1 destruct
29 elim (reqg_fqus_trans … H2 … HL1) -L // #L #T0 #H2 #HT02 #HL2
30 elim (teqg_fqus_trans … H2 … HT1) -T // #L0 #T #H2 #HT0 #HL0
31 lapply (teqg_reqg_conf_sn … HT02 … HL0) -HL0 // #HL0
32 /4 width=7 by feqg_intro_dx, reqg_trans, teqg_trans, ex2_3_intro/