
theorem Th5:
  for n,k be Nat, p be ExtReal st k <= 2|^n*n & n <= p holds k/(2|^n) <= p
proof
  let n,k be Nat;
  let p be ExtReal;
  assume that
A1: k <= 2|^n*n and
A2: n <= p;
  assume p < k/(2|^n);
  then n < k/(2|^n) by A2,XXREAL_0:2;
  hence contradiction by A1,PREPOWER:6,XREAL_1:79;
end;
