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

theorem
  k <= 2 * n implies (k+1) div 2 <= n
proof
  assume k <= 2 * n;
  then k + 1 <= 2 * n + 1 by XREAL_1:6;
  then (k + 1) div 2 <= (2 * n + 1) div 2 by Th24;
  hence thesis by NAT_D:def 1;
end;
