reserve a,b,c,d,x,j,k,l,m,n for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  a|^3-b|^3 = (a-b)*((a+b)*(a+b)+a|^2+b|^2)/2
  proof
    A1: a|^2 - b|^2 = (a-b)*(a+b) by Th1;
    a|^3 - b|^3 = a|^(2+1)-b|^(2+1)
    .=(a-b)*((a+b)*(a+b)+a|^2+b|^2)/2 by A1,Th14;
    hence thesis;
  end;
