Definition zip_unit f := 
  let: FinMap s pf := f in FinMap (zip_unit_sorted' pf).

Lemma zip_fnd f1 f2 f x (v : V) : zip f1 f2 = Some f -> fnd x f = Some v -> exists v1, exists v2, [/\ zip_f v1 v2 = Some v, fnd x f1 = Some v1 & fnd x f2 = Some v2].