(* Basic inversion lemmas ***************************************************)
-(* Basic_1: was: lifts1_flat (left to right) *)
lemma lifts_inv_applv1: ∀V1s,U1,T2,cs. ⬆*[cs] Ⓐ V1s. U1 ≡ T2 →
∃∃V2s,U2. ⬆*[cs] V1s ≡ V2s & ⬆*[cs] U1 ≡ U2 &
T2 = Ⓐ V2s. U2.
(* Basic properties *********************************************************)
-(* Basic_1: was: lifts1_flat (right to left) *)
lemma lifts_applv: ∀V1s,V2s,cs. ⬆*[cs] V1s ≡ V2s →
∀T1,T2. ⬆*[cs] T1 ≡ T2 →
⬆*[cs] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.