Definition  AnnDefEq_regularity :
    (forall G D g A B,   AnnDefEq G D g A B ->
                    exists C1 C2 g', AnnTyping G A C1 /\ AnnTyping G B C2
                                /\ AnnDefEq G (dom G) g' C1 C2) :=
  fourth AnnDefEqAnnIso_regularity.Definition AnnIso_regularity :
  forall G D g phi1 phi2, AnnIso G D g phi1 phi2 ->
                     AnnPropWff G phi1 /\ AnnPropWff G phi2 :=
  third AnnDefEqAnnIso_regularity.

Lemma erase_capp : forall AB0 C G, AnnTyping G AB0 C -> forall A, erase AB0 = (a_CAp