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|^n + u|^n = z|^n implies 2|^n divides (t*u*z)|^n
  proof
    assume t|^n + u|^n = z|^n; then
    t|^n + u|^n +(-z|^n) = 0; then
    t|^n + u|^n +(-z|^n) is even; then
    t|^n*u|^n*(-z|^n) is even by Th100; then
    -(t|^n*u|^n*z|^n) is even; then
    t|^n*u|^n*z|^n is even by INT_2:10; then
    t is even or u is even or z is even; then
    t*u*z is even;
    hence thesis by Th15;
  end;
