copy — Mathlib

English

The image of a LocalSubring under a ring homomorphism is again a LocalSubring.

Русский

Образ локального подполь кольца под кольтором снова является локальным подполь кольцом.

LaTeX

$$If f: R → S is a ring homomorphism and s is a LocalSubring R, then LocalSubring.map f s is a LocalSubring S.$$

Lean4

/-- Copy of a local subring with a new `carrier` equal to the old one.
Useful to fix definitional equalities. -/
protected def copy (S : LocalSubring R) (s : Set R) (hs : s = ↑S.toSubring) : LocalSubring R :=
  LocalSubring.mk (S.toSubring.copy s hs) (isLocalRing := hs ▸ S.2)

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