(* SUPPRESSION OF ALL OCCURRENCES of z: *)
Fixpoint Ds(s:set)(z:dart){struct s}:set:=
match s with
Vs => Vs
| Is s0 x =>
if eq_dart_dec x z then (Ds s0 z)
else Is (Ds s0 z) x
end.

(* Specifications: *)
Lemma not_exds_Ds:forall(s:set)(z:dart),
~exds (Ds s z) z.
Lemma exds_Ds:forall(s:set)(x z:dart),
x <> z ->
(exds s z <-> exds (Ds s x) z).
Lemma exds_Ds_diff:forall(s:set)(x z:dart),
exds (Ds s x) z -> x <> z.