isAlgebraic_algebraMap — Mathlib

English

If r is transcendental and f is transcendental, then aeval r f is transcendental.

Русский

Если r трансцендентен, а f трансцендентен, то aeval r f трансцендентен.

LaTeX

$$$ \forall r : A\ (H : Transcendental R r) \to \forall f : R[X],\ Transcendental R f \to Transcendental R (Polynomial.aeval r f) $$$

Lean4

/-- An element of `R` is algebraic, when viewed as an element of the `R`-algebra `A`. -/
theorem isAlgebraic_algebraMap [Nontrivial R] (x : R) : IsAlgebraic R (algebraMap R A x) :=
  ⟨_, X_sub_C_ne_zero x, by rw [map_sub, aeval_X, aeval_C, sub_self]⟩

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