(* Properties on lazy equivalence for local environments ********************)
+lemma llpx_lrefl: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2.
+/2 width=1 by llpx_sn_lrefl/ qed-.
+
lemma lleq_llpx_trans: ∀h,g,G,L1,L2,T,d. L1 ⋕[T, d] L2 →
∀L.⦃G, L2⦄ ⊢ ➡[h, g, T, d] L → ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L.
/3 width=3 by lleq_cpx_trans, lleq_llpx_sn_trans/ qed-.