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[Merged by Bors] - feat(data/nat/factorization): add lemma factorization_prod
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Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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For any `p : ℕ` and any function `g : α → ℕ` that's non-zero on `S : finset α`, the power of `p` in `S.prod g` equals the sum over `x ∈ S` of the powers of `p` in `g x`. Generalises `factorization_mul`, which is the special case where `S.card = 2` and `g = id`.
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factorization_prodfactorization_prod
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For any
p : ℕand any functiong : α → ℕthat's non-zero onS : finset α, the power ofpinS.prod gequals the sum overx ∈ Sof the powers ofping x.Generalises
factorization_mul, which is the special case whereS.card = 2andg = id.