bijective_extensionEmbeddingOfIsReal

English

If the infinite place v is real, the extension embedding from v.Completion to ℝ is bijective.

Русский

Если бесконечнаяPlacement v реален, вложение v.Completion в ℝ биективно.

LaTeX

$$$\text{IsReal}(v) \Rightarrow \text{Function.Bijective}(\text{extensionEmbeddingOfIsReal}(hv))$$$

Lean4

/-- If `v` is a real infinite place, then the embedding `v.Completion →+* ℝ` is bijective. -/
theorem bijective_extensionEmbeddingOfIsReal {v : InfinitePlace K} (hv : IsReal v) :
    Function.Bijective (extensionEmbeddingOfIsReal hv) :=
  ⟨(extensionEmbeddingOfIsReal hv).injective, surjective_extensionEmbeddingOfIsReal hv⟩

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