+interpretation
+ "parallel rt-transition (full local environment)"
+ 'PRedSn h G L1 L2 = (lpr h G L1 L2).
+
+(* Basic properties *********************************************************)
+
+lemma lpr_bind (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ➡[h] K2 →
+ ∀I1,I2. ⦃G, K1⦄ ⊢ I1 ➡[h] I2 → ⦃G, K1.ⓘ{I1}⦄ ⊢ ➡[h] K2.ⓘ{I2}.
+/2 width=1 by lex_bind/ qed.
+
+(* Note: lemma 250 *)
+lemma lpr_refl (h) (G): reflexive … (lpr h G).
+/2 width=1 by lex_refl/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma lpr_bind_refl_dx (h) (G): ∀K1,K2. ⦃G, K1⦄ ⊢ ➡[h] K2 →
+ ∀I. ⦃G, K1.ⓘ{I}⦄ ⊢ ➡[h] K2.ⓘ{I}.
+/2 width=1 by lex_bind_refl_dx/ qed.
+
+lemma lpr_pair (h) (G): ∀K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h] V2 →
+ ∀I. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h] K2.ⓑ{I}V2.
+/2 width=1 by lex_pair/ qed.