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

(* Specifications: *)
Lemma AnnTyping_lc1 : forall G a A, AnnTyping G a A -> lc_tm a.
Lemma AnnTyping_lc2 : forall G a A, AnnTyping G a A -> lc_tm A.
Lemma AnnIso_lc1 : forall G D g p1 p2, AnnIso G D g p1 p2 -> lc_constraint p1.
Lemma AnnIso_lc2 : forall G D g p1 p2, AnnIso G D g p1 p2 -> lc_constraint p2.
Lemma AnnIso_lc3 : forall G D g p1 p2, AnnIso G D g p1 p2 -> lc_co g.
Lemma AnnDefEq_lc1 : forall G D g A B, AnnDefEq G D g A B -> lc_tm A.
Lemma AnnDefEq_lc2 : forall G D g A B, AnnDefEq G D g A B -> lc_tm B.
Lemma AnnDefEq_lc3 : forall G D g A B, AnnDefEq G D g A B -> lc_co g.
Lemma AnnToplevel_lc : forall c s, binds c s an_toplevel -> lc_sig_sort s.