-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.
+lemma cpxs_teqx_fpbs_trans:
+ ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T → ∀T0. T ≛ T0 →
+ ∀G2,L2,T2. ❪G1,L1,T0❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=3 by cpxs_fpbs_trans, teqx_fpbs_trans/ qed-.
+
+lemma cpxs_teqx_fpbs:
+ ∀G,L,T1,T. ❪G,L❫ ⊢ T1 ⬈* T →
+ ∀T2. T ≛ T2 → ❪G,L,T1❫ ≥ ❪G,L,T2❫.
+/4 width=3 by cpxs_fpbs_trans, feqx_fpbs, teqx_feqx/ qed.