lemma lpxs_pair_refl: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡*[h, g] L2.ⓑ{I}V.
/2 width=1 by TC_lpx_sn_pair_refl/ qed.
lemma lpxs_pair_refl: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡*[h, g] L2.ⓑ{I}V.
/2 width=1 by TC_lpx_sn_pair_refl/ qed.