ringEquivRealOfIsReal — Mathlib

English

If the infinite place v is real, there exists a ring isomorphism from v.Completion to ℝ.

Русский

Если бесконечная Placament v реален, существует кольцевой изоморфизм v.Completion ≃+* ℝ.

LaTeX

$$$\text{IsReal}(v) \Rightarrow v.Completion \cong_{+*} \mathbb{R}$$$

Lean4

/-- The ring isomorphism `v.Completion ≃+* ℝ`, when `v` is real, given by the bijection
`v.Completion →+* ℝ`. -/
def ringEquivRealOfIsReal {v : InfinitePlace K} (hv : IsReal v) : v.Completion ≃+* ℝ :=
  RingEquiv.ofBijective _ (bijective_extensionEmbeddingOfIsReal hv)

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