reserve a,b,i,j,k,l,m,n for Nat;

theorem EZ:
  (n!)*(k!) = (n+k)! iff (n = 0 or k = 0)
  proof
    n = (n+k) - k & n+k >= 0+k by XREAL_1:6; then
    ((n+k) choose (k*1))*((n!)*(k!)) = (n+k)!/((n!)*(k!))*((n!)*(k!))
      by NEWTON:def 3
    .= (n+k)! by XCMPLX_1:87;
    hence thesis by NCK,XCMPLX_1:7;
  end;
