lemma lfpxs_step_dx: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
/2 width=3 by tc_lfxs_step_dx/ qed.
lemma lfpxs_step_dx: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
/2 width=3 by tc_lfxs_step_dx/ qed.