(* Properties on equivalence for local environments *************************)
lemma leq_lleq_trans: ∀L2,L,T,d. L2 ≡[T, d] L →
- â\88\80L1. L1 â\89\83[d, ∞] L2 → L1 ≡[T, d] L.
+ â\88\80L1. L1 ⩬[d, ∞] L2 → L1 ≡[T, d] L.
/2 width=3 by leq_llpx_sn_trans/ qed-.
lemma lleq_leq_trans: ∀L,L1,T,d. L ≡[T, d] L1 →
- â\88\80L2. L1 â\89\83[d, ∞] L2 → L ≡[T, d] L2.
+ â\88\80L2. L1 ⩬[d, ∞] L2 → L ≡[T, d] L2.
/2 width=3 by llpx_sn_leq_trans/ qed-.
-lemma lleq_leq_repl: â\88\80L1,L2,T,d. L1 â\89¡[T, d] L2 â\86\92 â\88\80K1. K1 â\89\83[d, ∞] L1 →
- â\88\80K2. L2 â\89\83[d, ∞] K2 → K1 ≡[T, d] K2.
+lemma lleq_leq_repl: â\88\80L1,L2,T,d. L1 â\89¡[T, d] L2 â\86\92 â\88\80K1. K1 ⩬[d, ∞] L1 →
+ â\88\80K2. L2 ⩬[d, ∞] K2 → K1 ≡[T, d] K2.
/2 width=5 by llpx_sn_leq_repl/ qed-.
lemma lleq_bind_repl_SO: ∀I1,I2,L1,L2,V1,V2,T. L1.ⓑ{I1}V1 ≡[T, 0] L2.ⓑ{I2}V2 →