Module Type ext_weak_sig.
Include ext_wf_sig.

Axiom respects_atoms_eq_mutual :
(forall G a A,     Typing  G a A       -> True) /\
(forall G phi,     PropWff G phi       -> True) /\
(forall G D p1 p2, Iso G D p1 p2 -> forall D', D [=] D' -> Iso G D' p1 p2) /\
(forall G D A B T,   DefEq G D A B T  -> forall D', D [=] D' -> DefEq G D' A B T) /\
(forall G,           Ctx G           -> True).