
theorem MDF1:
  for n,k be Nat holds (min (n,k))! divides n!
  proof
    let n,k be Nat;
    reconsider m = min (n,k) as Nat;
    n - m >= m - m by XREAL_1:9,XXREAL_0:17; then
    reconsider d = n - m as Nat;
    m! divides (m + d)! by MDF;
    hence thesis;
  end;
