fintypeRange — Mathlib

English

The coercion of the Infimum over a set of subrings equals the Infimum taken pointwise as sets.

Русский

Приведение Infimum для множества подполосов равна Infimum взятое по точкам как множество.

LaTeX

$$$$\big((\,sInf\, S) : \mathrm{NonUnitalSubring}\, R\big) = \bigcap_{s \in S} s.$$$$

Lean4

/-- The range of a ring homomorphism is a fintype, if the domain is a fintype.
Note: this instance can form a diamond with `Subtype.fintype` in the
  presence of `Fintype S`. -/
instance fintypeRange [Fintype R] [DecidableEq S] (f : R →ₙ+* S) : Fintype (range f) :=
  Set.fintypeRange f

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