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

Lemma zip_filter' s1 s2 s x : zip' s1 s2 = Some s -> zip' (filter (predCk V x) s1) (filter (predCk V x) s2) = Some (filter (predCk V x) s).