-lemma cpxs_teqx_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, feqx_fpbs, teqx_feqx/ 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.