-lemma cpxs_tdeq_fpbs: ∀h,G,L,T1,T. ⦃G,L⦄ ⊢ T1 ⬈*[h] T →
- ∀T2. T ≛ T2 → ⦃G,L,T1⦄ ≥[h] ⦃G,L,T2⦄.
-/4 width=3 by cpxs_fpbs_trans, fdeq_fpbs, tdeq_fdeq/ qed.
-
-(* Properties with star-iterated structural successor for closures **********)
-
-lemma cpxs_fqus_fpbs: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
- ∀G2,L2,T2. ⦃G1,L1,T⦄ ⬂* ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃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.