Definition AnnTyping_AnnCtx  := first  ann_ctx_wff_mutual.Definition AnnPropWff_AnnCtx := second ann_ctx_wff_mutual.Definition AnnIso_AnnCtx     := third  ann_ctx_wff_mutual.Definition AnnDefEq_AnnCtx   := fourth ann_ctx_wff_mutual.

Lemma lc_mutual : (forall G0 a A, AnnTyping G0 a A -> lc_tm a /\ lc_tm A) /\ (forall G0 phi, AnnPropWff G0 phi -> lc_constraint phi) /\ (forall G0 D g p1 p2, AnnIso G0 D g p1 p2 -> lc_constraint p1 /\ lc_constraint p2 /\ lc_co g) /\ (forall G0 D g A B, AnnDefEq G0 D g A B -> lc_tm A /\ lc_tm B /\ lc_co g) /\ (forall G0, AnnCtx G0 -> forall x s , binds x s G0 -> lc_sort s).