lemma lpqs_refl: ∀L. L ⊢ ➤* L.
/2 width=1 by lpx_sn_refl/ qed.
+lemma lpqs_pair: ∀I,K1,K2,V1,V2. K1 ⊢ ➤* K2 → K1 ⊢ V1 ➤* V2 →
+ K1.ⓑ{I}V1 ⊢ ➤* K2.ⓑ{I}V2.
+/2 width=1/ qed.
+
lemma lpqs_append: ∀K1,K2. K1 ⊢ ➤* K2 → ∀L1,L2. L1 ⊢ ➤* L2 →
L1 @@ K1 ⊢ ➤* L2 @@ K2.
/3 width=1 by lpx_sn_append, cpqs_append/ qed.