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 be non trivial odd Nat holds
    a|^n + a|^n < a|^(n+1)
  proof
    let a be non trivial odd Nat;
    a - 1 <> 1 & a - 1 <> 0; then
    reconsider b = a-1 as non trivial Nat by NAT_2:def 1;
    (b+1)|^n + (b+1)|^n < (b+1)|^(n+1) by LmNT;
    hence thesis;
  end;
