isRoot_of_aeval_algebraMap_eq_zero

English

If algebraMap R S is injective and aeval (algebraMap R S r) p = 0, then p has r as a root.

Русский

Если алгебраMap R S инъективен и aeval(алгебраMap R S r) p = 0, то p имеет корнем r.

LaTeX

$$inj : Injective (algebraMap R S) → aeval (algebraMap R S r) p = 0 → p.IsRoot r$$

Lean4

theorem isRoot_of_aeval_algebraMap_eq_zero [Algebra R S] {p : R[X]} (inj : Function.Injective (algebraMap R S)) {r : R}
    (hr : aeval (algebraMap R S r) p = 0) : p.IsRoot r :=
  isRoot_of_eval₂_map_eq_zero inj hr

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