coe_injective — Mathlib

English

The canonical map algebraMap: 𝓞K → K is injective; i.e., distinct elements of 𝓞K have distinct images in K.

Русский

Каноническое отображение algebraMap: 𝓞K → K инъективно; различные элементы 𝓞K имеют различные образы в K.

LaTeX

$$$\\operatorname{Injective}(\\mathrm{algebraMap}_{\\mathcal{O}_K,K})$$$

Lean4

/-- The canonical map from `𝓞 K` to `K` is injective.

This is a convenient abbreviation for `FaithfulSMul.algebraMap_injective`.
-/
theorem coe_injective : Function.Injective (algebraMap (𝓞 K) K) :=
  FaithfulSMul.algebraMap_injective _ _

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