reserve i, j, k, l, m, n, t for Nat;

theorem
  k <= n implies 2 to_power k divides 2 to_power n
proof
  assume k <= n;
  then
A2: 2 to_power n = (2 to_power k) * (2 to_power (n-'k)) by Th10;
  reconsider a = 2 to_power (n-'k) as Nat by TARSKI:1;
  take a;
  thus thesis by A2;
end;
