English
If f is monic, the canonical map from AdjoinRoot f to itself derived from monicity equals the standard mk map: (AdjoinRoot.isAdjoinRootMonic f hf).map = AdjoinRoot.mk f.
Русский
Если f моноическая, каноническое отображение от AdjoinRoot f к самому себе, полученное из моничности, равно стандартной карте-образу: (AdjoinRoot.isAdjoinRootMonic f hf).map = AdjoinRoot.mk f.
LaTeX
$$$ (AdjoinRoot.isAdjoinRootMonic f hf).map = AdjoinRoot.mk f $$$
Lean4
/-- `AdjoinRoot f` is indeed given by adjoining a root of `f`. -/
protected def isAdjoinRoot : IsAdjoinRoot (AdjoinRoot f) f
where
map := AdjoinRoot.mkₐ f
map_surjective := Ideal.Quotient.mkₐ_surjective _ _
ker_map := by ext; simp [Ideal.mem_span_singleton]
