Slate - Power of identity to integer is identity

Proposition 1.5.37. Let X be a set, a ∈ ℤ. Then:

(id_X)^a = id_X

Proof.

Assume a ≥ 0. Then (id_X)^a = id_X by 1.5.36.
Assume a < 0. Then:
((id_X)^-1)^−a =^1.5.33 (id_X)^−a =^1.5.36 id_X