[Merged by Bors] - refactor(ring_theory/perfection): remove coercion in the definition of the type #7583
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| /-- The perfection of a ring `R` with characteristic `p`, as a subring, | ||
| defined to be the projective limit of `R` using the Frobenius maps `R → R` | ||
| indexed by the natural numbers, implemented as `{ f : ℕ → R | ∀ n, f (n + 1) ^ p = f n }`. -/ | ||
| def ring.perfection_subring (R : Type u₁) [comm_ring R] | ||
| (p : ℕ) [hp : fact p.prime] [char_p R p] : | ||
| subring (ℕ → R) := | ||
| (ring.perfection_subsemiring R p).to_subring $ λ n, by simp_rw [← frobenius_def, pi.neg_apply, | ||
| pi.one_apply, ring_hom.map_neg, ring_hom.map_one] |
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Note that we actually had this definition before (https://github.com/leanprover-community/mathlib/pull/5386/files#r544380327) and with a shorter proof too; but it was deemed not useful and inlined into the two places that used it.
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…f the type (#7583) Defining the type `ring.perfection R p` as a plain subtype (but inheriting the semiring or ring instances from a `subsemiring` structure) removes several coercions and helps Lean a lot when elaborating or unifying.
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Defining the type
ring.perfection R pas a plain subtype (but inheriting the semiring or ring instances from asubsemiringstructure) removes several coercions and helps Lean a lot when elaborating or unifying.