theorem
  a|^2 + b|^2 = c|^2 implies ex t st b|^2 = (2*a+t)*t
  proof
    assume a|^2+b|^2 = c|^2; then
    b|^2 = c|^2 - a|^2
    .= (c-a)*(c+a) by NEWTON01:1
    .= (c-a)*((c-a)+2*a);
    hence thesis;
  end;
