∀n1,T1. ⦃G,L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L0⦄ ⊢ T0 ➡*[n2,h] T2 →
∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
(* Auxiliary properties for preservation ************************************)
∀n1,T1. ⦃G,L0⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L0⦄ ⊢ T0 ➡*[n2,h] T2 →
∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
(* Auxiliary properties for preservation ************************************)