inversion 1; subst; solve_uniq.
Qed.
Hint Resolve Ctx_uniq.

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).