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_a_Const : forall G0 a0 A0 A1 T, erase a0 = a_Const T -> binds T (Cs A1) an_toplevel ->