Definition AnnPropWff_lc := second lc_mutual.
Definition AnnIso_lc     := third lc_mutual.
Definition AnnDefEq_lc   := fourth lc_mutual.
Definition AnnCtx_lc     := fifth lc_mutual.

Lemma AnnTyping_lc2 : forall G a A, AnnTyping G a A -> lc_tm A.
intros G a A H. destruct (AnnTyping_lc H); auto.