reserve X for non empty CUNITSTR;
reserve a, b for Complex;
reserve x, y for Point of X;
reserve X for ComplexUnitarySpace;
reserve x, y, z, u, v for Point of X;

theorem
  (x-y).|.(u-v) = x.|.u - x.|.v - y.|.u + y.|.v
proof
  (x - y) .|. (u - v) = x .|. (u - v) - y .|. (u - v) by Th21
    .= ( x .|. u - x .|. v ) - y .|. (u - v) by Th22
    .= ( x .|. u - x .|. v ) - ( y .|. u - y .|. v ) by Th22;
  hence thesis;
end;
