Section g_eill_complete.
Variable (Σ : list eill_cmd) (Γ : list eill_vars).
Notation vars := (flat_map eill_cmd_vars Σ ++ Γ).
Let vv := nat_sort vars.
Let Hvv1 : list_injective vv.
Variables (x : eill_vars)
(Hvalid : forall n s, @ill_sequent_tps n s (map (fun c => !⦑c⦒) Σ ++ map £ Γ) (£ x) vec_zero).

Theorem G_eill_complete : Σ; Γ ⊦ x.