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.

Lemma lc_mutual : (forall G0 a A, Typing G0 a A -> lc_tm a /\ lc_tm A) /\ (forall G0 phi, PropWff G0 phi -> lc_constraint phi) /\ (forall G0 D p1 p2, Iso G0 D p1 p2 -> lc_constraint p1 /\ lc_constraint p2) /\ (forall G0 D A B T, DefEq G0 D A B T -> lc_tm A /\ lc_tm B /\ lc_tm T) /\ (forall G0, Ctx G0 -> forall x s , binds x s G0 -> lc_sort s).