(* OK: *)

Lemma rem_1_step :forall(m:fmap)(z:dart)(s:set),
inv_hmap m ->
let sr:= Iter_rem_aux m z s in
let nr:= Iter_upb_aux m z s in
(card sr + 1 <= card s <->
exds s (Iter (f m) (ndN m - card s) z))%nat.