theorem
  for x holds bD(AffineMap(a,b),h).x = a*h
proof
  let x;
  bD(AffineMap(a,b),h).x = AffineMap(a,b).x-AffineMap(a,b).(x-h) by DIFF_1:4
    .= a*x+b-AffineMap(a,b).(x-h) by FCONT_1:def 4
    .= a*x+b-(a*(x-h)+b) by FCONT_1:def 4;
  hence thesis;
end;
