Module pres := fc_preservation wf weak subst e_subst.
(* Why does this cause so many messages? *)

Lemma erased_tm_erase_mutual :
(forall G0 a B (H : AnnTyping G0 a B),
erased_tm (erase a) /\ erased_tm (erase B)) /\
(forall G0 phi (H : AnnPropWff G0 phi),
forall a b A, phi = (Eq a b A) ->
erased_tm (erase a) /\ erased_tm (erase b)
/\ erased_tm (erase A)) /\
(forall G0 D g p1 p2 (H : AnnIso G0 D g p1 p2),
True) /\
(forall  G0 D g A B (H : AnnDefEq G0 D g A B),
True) /\
(forall G0 (H : AnnCtx G0),
forall x A, binds x (Tm A) G0 -> erased_tm (erase_tm A)
).