neg — Mathlib

English

Let ϕ: L →ₐ[K] L be a K-algebra homomorphism with [FiniteDimensional K L]. Then ϕ is bijective.

Русский

Пусть ϕ: L →ₐ[K] L — алгебраический гомоморфизм с [FiniteDimensional K L]. Тогда ϕ биективен.

LaTeX

$$$[FiniteDimensional K L]\Rightarrow (\forall ϕ: L →ₐ[K] L, Function.Bijective\ ϕ)$$$

Lean4

protected theorem neg : IsAlgebraic R (-a) :=
  have ⟨p, h, eval0⟩ := ha
  ⟨algEquivAevalNegX p, EmbeddingLike.map_ne_zero_iff.mpr h, by simpa [← comp_eq_aeval, aeval_comp]⟩

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