Notation nil := (nil K V).Definition fnd k (s : fmap) :=
  if (filter (predk k) (seq_of s)) is (_, v):: _
  then Some v else None.

Lemma path_ins' s k1 k2 v : ord k1 k2 -> path ord k1 (map key s) -> path ord k1 (map key (ins' k2 v s)).