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 Th28:
  (x-y).|.(x-y) = x.|.x - x.|.y - y.|.x + y.|.y
proof
  (x - y) .|. (x - y) = x .|. (x - y) - y .|. (x - y) by Th21
    .= x .|. x - x .|. y - y .|. (x - y) by Th22
    .= x.|.x - x.|.y - ( y.|.x - y.|.y ) by Th22;
  hence thesis;
end;
