(* ---------------- regularity lemmas ------------------- *)

(* Specifications: *)
Axiom Typing_regularity: forall e A G, Typing G e A -> Typing G A a_Star.
Axiom DefEq_regularity :
forall G D A B T, DefEq G D A B T -> PropWff G (Eq A B T).
Axiom Iso_regularity :
forall G D phi1 phi2, Iso G D phi1 phi2 -> PropWff G phi1 /\ PropWff G phi2.
Axiom PropWff_regularity :
forall G A B T, PropWff G (Eq A B T) ->  Typing G A T /\ Typing  G B T.