∀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 →
∀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 →