theorem
  (a*s + b*t)`1 = a * s`1 + b * t`1
proof
  thus (a*s+b*t)`1 = (a*s)`1 + (b*t)`1 by TOPREAL3:2
    .= a*s`1 + (b*t)`1 by TOPREAL3:4
    .= a*s`1+b*t`1 by TOPREAL3:4;
end;
