Lemma ann_ctx_wff_mutual : (forall G0 a A, AnnTyping G0 a A -> AnnCtx G0) /\ (forall G0 phi, AnnPropWff G0 phi -> AnnCtx G0) /\ (forall G0 D g p1 p2, AnnIso G0 D g p1 p2 -> AnnCtx G0) /\ (forall G0 D g A B, AnnDefEq G0 D g A B -> AnnCtx G0) /\ (forall G0, AnnCtx G0 -> True).