(* Basic_2A1: includes: aaa_inv_lift *)
lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀b,f,L1. ⬇*[b, f] L2 ≡ L1 →
∀T1. ⬆*[f] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A.
(* Basic_2A1: includes: aaa_inv_lift *)
lemma aaa_inv_lifts: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀b,f,L1. ⬇*[b, f] L2 ≡ L1 →
∀T1. ⬆*[f] T1 ≡ T2 → ⦃G, L1⦄ ⊢ T1 ⁝ A.