Definition Typing_Ctx  := first  ctx_wff_mutual.
Definition PropWff_Ctx := second ctx_wff_mutual.
Definition Iso_Ctx     := third  ctx_wff_mutual.
Definition DefEq_Ctx   := fourth ctx_wff_mutual.
(* TODO: put these hints in a database? *)
Hint Resolve Typing_Ctx PropWff_Ctx Iso_Ctx DefEq_Ctx.

(* Specifications: *)
Lemma Ctx_uniq : forall G, Ctx G -> uniq G.
induction G; try auto.