Section binomial.
Infix "<d" := divides (at level 70, no associativity).
Hint Resolve divides_refl : core.
Let fact_neq_0 n : fact n <> 0.
Fact binomial_gt n : forall p, n < p -> binomial n p = 0.
Fact binomial_nn n : binomial n n = 1.

Theorem binomial_thm n p : p <= n -> fact n = binomial n p * fact p * fact (n-p).