reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  (t+u-z)|^3,(t|^3+u|^3-z|^3) are_congruent_mod 3
  proof
    2*1+1 is odd; then
    A1: (-z)|^3 = -z|^3 by POWER:2;
    (t+u+(-z))|^3,(t|^3+u|^3+(-z)|^3) are_congruent_mod 3 by LmTUZ;
    hence thesis by A1;
  end;
