-lemma cpxs_tdeq_fpbs: ∀h,o,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬈*[h] T →
- ∀T2. T ≛[h, o] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/4 width=3 by cpxs_fpbs_trans, ffdeq_fpbs, tdeq_ffdeq/ qed.
-
-(* Properties with star-iterated structural successor for closures **********)
-
-lemma cpxs_fqus_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
- ∀G2,L2,T2. ⦃G1, L1, T⦄ ⊐* ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbs_fqus_trans, cpxs_fpbs/ qed.
+lemma cpxs_teqg_fpbs (S):
+ reflexive … S → symmetric … S →
+ ∀G,L,T1,T. ❨G,L❩ ⊢ T1 ⬈* T →
+ ∀T2. T ≛[S] T2 → ❨G,L,T1❩ ≥ ❨G,L,T2❩.
+/4 width=5 by cpxs_fpbs_trans, feqg_fpbs, teqg_feqg/ qed.