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

theorem
  for a, b be non zero Nat, n be non trivial Nat holds
    (a+b) |-count (a|^n + b|^n) < n
  proof
    let a,b be non zero Nat, n be non trivial Nat;
    reconsider m = n - 1 as non zero Nat;
    (a+b)|^1 = a|^1 + b|^1; then
    (a+b)|^(1+m) > a|^(1+m) + b|^(1+m) by NEWTON01:18;
    hence thesis by Count4;
  end;
