Definition AnnIso_respects_atoms_eq   := third  ann_respects_atoms_eq_mutual.
Definition AnnDefEq_respects_atoms_eq := fourth ann_respects_atoms_eq_mutual.

Axiom AnnDefEq_weaken_available :
forall G D g A B, AnnDefEq G D g A B -> AnnDefEq G (dom G) g A B.