
theorem
  for n,k be Nat holds k >= 2*n implies 2|^n divides k!
  proof
    let n,k be Nat;
    assume k >= 2*n; then
    min (k,2*n) = 2*n by XXREAL_0:def 9; then
    A1: (2*n)! divides k! by MDF1;
    (2!)|^n divides (2*n)! by FPD;
    hence thesis by A1,INT_2:9;
  end;
