aeval_algebraMap_apply — Mathlib

English

For any x ∈ A and p ∈ R[X], aeval (algebraMap A B x) p = algebraMap A B (aeval x p).

Русский

Для любой x ∈ A и p ∈ R[X], aeval(алгебраMap_A_B x) p = algebraMap_A_B (aeval x p).

LaTeX

$$$$\\mathrm{aeval}_{\\mathrm{algebraMap}_{A\\to B}(x)}(p) = \\mathrm{algebraMap}_{A\\to B}(\\mathrm{aeval}_x(p)).$$$$

Lean4

theorem aeval_algebraMap_apply (x : A) (p : R[X]) : aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
  rw [aeval_def, aeval_def, hom_eval₂, ← IsScalarTower.algebraMap_eq]

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