Invertibility of factorials #
This file contains lemmas providing sufficient conditions for the cast of n!
to a (semi)ring A
to be a unit.
theorem
IsUnit.natCast_of_isNilpotent_of_coprime
{A : Type u_1}
[CommRing A]
{n p : ℕ}
(hp : IsNilpotent ↑p)
(h : p.Coprime n)
:
IsUnit ↑n
theorem
Nat.castChoose_eq
{A : Type u_1}
[CommSemiring A]
{m : ℕ}
{k : ℕ × ℕ}
(hm : IsUnit ↑m.factorial)
(hk : k ∈ Finset.antidiagonal m)
: