Definition expnDn := Pascal.

(* Specifications: *)
Lemma Vandermonde k l i :
\sum_(j < i.+1) 'C(k, j) * 'C(l, i - j) = 'C(k + l , i).
Lemma subn_exp m n k :
m ^ k - n ^ k = (m - n) * (\sum_(i < k) m ^ (k.-1 -i) * n ^ i).
Lemma predn_exp m k : (m ^ k).-1 = m.-1 * (\sum_(i < k) m ^ i).
Lemma dvdn_pred_predX n e : (n.-1 %| (n ^ e).-1)%N.
Section Combinations.