(* This version of the proof is incredibly slow. *)
(* all: pre; basic_solve. all: try oh_c'mon. all: try invert_open_wrt. all: try pick fresh c for L. all: try eapply lc_a_UCAbs_exists; eauto. all: try apply H; eauto. all: eapply (lc_a_UAbs_exists c). rewrite e. eauto. done. Qed.*)
Definition Typing_lc  := first lc_mutual.
Definition PropWff_lc := second lc_mutual.
Definition Iso_lc     := third lc_mutual.
Definition DefEq_lc   := fourth lc_mutual.
Definition Ctx_lc     := fifth lc_mutual.

Lemma Typing_lc1 : forall G0 a A, Typing G0 a A -> lc_tm a.