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;
