-lemma lpr_pair: ∀I,K1,K2,V1,V2. K1 ⊢ ➡ K2 → K1 ⊢ V1 ➡ V2 →
- K1.ⓑ{I}V1 ⊢ ➡ K2.ⓑ{I}V2.
-/2 width=1/ qed.
-
-lemma lpr_append: ∀K1,K2. K1 ⊢ ➡ K2 → ∀L1,L2. L1 ⊢ ➡ L2 →
- L1 @@ K1 ⊢ ➡ L2 @@ K2.
-/3 width=1 by lpx_sn_append, cpr_append/ qed.
-
-lemma lpqs_lpr: ∀L1,L2. L1 ⊢ ➤* L2 → L1 ⊢ ➡ L2.
-#L1 #L2 #H elim H -L1 -L2 // /3 width=1/
-qed.
-
-lemma lpss_lpr: ∀L1,L2. L1 ⊢ ▶* L2 → L1 ⊢ ➡ L2.
-/3 width=1/ qed.
+lemma lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 →
+ ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
+/2 width=1 by lpx_sn_pair/ qed.