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3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "static_2/static/reqg_reqg.ma".
16 include "static_2/static/req.ma".
17
18 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
19
20 (* Advanced Forward lemmas **************************************************)
21
22 lemma req_rex_trans (R) (L) (T):
23       R_transitive_req R →
24       ∀L1. L1 ≡[T] L → ∀L2. L ⪤[R,T] L2 → L1 ⪤[R,T] L2.
25 #R #L #T #HR #L1 #HL1 #L2 #HL2
26 @(rex_trans_fsle … HL1 … HL2) -L (**) (* fulll auto too slow *)
27 /3 width=16 by transitive_req_fwd_rex, reqg_fsle_comp, rex_trans_next/
28 qed-.
29
30 lemma req_reqg_trans (S) (T:term) (L):
31       ∀L1. L1 ≡[T] L → ∀L2. L ≛[S,T] L2 → L1 ≛[S,T] L2.
32 /2 width=3 by req_rex_trans/ qed-.