feat(algebra/char_p/basic): refactor proof of add_pow_char_of_commute to extract a statement true in all rings (#11364)
If x and y commute, the pth power of their sum is the sum of the pth powers plus a multiple of p.
This holds in any semiring and easily implies the additivity of frobenius in char p, but is occasionally useful in characteristic 0.
Also make the fact that p is 0 in a char_p ring a simp lemma.
From flt-regular
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Yaƫl Dillies <yael.dillies@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>