reserve x, x1, x2, y, X, D for set,
  i, j, k, l, m, n, N for Nat,
  p, q for XFinSequence of NAT,
  q9 for XFinSequence,
  pd, qd for XFinSequence of D;

theorem Th26:
  m <= n implies n choose m > 0
proof
  assume
A1: m<=n;
  then reconsider nm=n-m as Nat by NAT_1:21;
A2: (m!)*(nm!)>(m!)*0 by XREAL_1:68;
  n!>0*((m!)*(nm!));
  then (n!)/((m!)*(nm!))>0 by A2,XREAL_1:81;
  hence thesis by A1,NEWTON:def 3;
end;
