(*  ----------------------------------------------------------- *)

Lemma annotation_mutual :
(forall G a A, Typing G a A ->
forall G0, erase_context G0 = G -> AnnCtx G0 ->
exists a0 A0,
(erase a0) = a /\
(erase A0) = A /\
AnnTyping G0 a0 A0) /\
(forall G phi, PropWff G phi ->
forall G0, erase_context G0 = G -> AnnCtx G0 ->
exists phi0,
erase_constraint phi0 = phi /\
AnnPropWff G0 phi0) /\
(forall G D p1 p2, Iso G D p1 p2 ->
forall G0, erase_context G0 = G -> AnnCtx G0 ->
exists g0 p1' p2',
(erase_constraint p1') = p1 /\
(erase_constraint p2') = p2 /\
AnnIso G0 D g0 p1' p2') /\
(forall G D a b A, DefEq G D a b A ->
forall G0, erase_context G0 = G -> AnnCtx G0 ->
exists g a0 b0 A0,
(erase a0) = a /\
(erase b0) = b /\
(erase A0) = A /\
AnnDefEq G0 D g a0 b0 /\ AnnTyping G0 a0 A0 /\ AnnTyping G0 b0 A0) /\
(forall G, Ctx G -> True).