reserve x,y for set,
  n,m for Nat,
  r,s for Real;

theorem
  for f,g be FinSequence holds f^g, g^f are_fiberwise_equipotent
proof
  let f,g be FinSequence;
  let y be object;
  thus card Coim(f^g,y) = card(g"{y})+ card(f"{y}) by FINSEQ_3:57
    .= card Coim(g^f,y) by FINSEQ_3:57;
end;
