injective_of_transcendental — Mathlib

English

For any a in S, if a is algebraic over R, then algebraMap S A a is algebraic over R.

Русский

Для любого a ∈ S, если a алгебраичен над R, тогда algebraMap S A a алгебраичен над R.

LaTeX

$$$ \forall a : S, IsAlgebraic R a \to IsAlgebraic R (algebraMap S A a) $$$

Lean4

theorem injective_of_transcendental [h : Algebra.Transcendental R A] : Function.Injective (algebraMap R A) :=
  by
  rw [transcendental_iff_not_isAlgebraic] at h
  contrapose! h
  exact isAlgebraic_of_not_injective h

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