theorem
  (a*s + b*t)`2 = a * s`2 + b * t`2
proof
  thus (a*s+b*t)`2 = (a*s)`2 + (b*t)`2 by TOPREAL3:2
    .= a*s`2 + (b*t)`2 by TOPREAL3:4
    .= a*s`2+b*t`2 by TOPREAL3:4;
end;
