of_algebraMap_bijective — Mathlib

English

If the algebra map R → S is bijective, then the zero relative dimension case gives IsStandardSmoothOfRelativeDimension 0.

Русский

Если отображение алгебраMap R → S биективно, то в нуле относительная размерность дает IsStandardSmoothOfRelativeDimension 0.

LaTeX

$$$\text{algebraMap } R S \text{ bijective} \Rightarrow \mathrm{IsStandardSmoothOfRelativeDimension}(0,R,S)$$$

Lean4

theorem of_algebraMap_bijective (h : Function.Bijective (algebraMap R S)) : IsStandardSmoothOfRelativeDimension 0 R S :=
  ⟨_, _, _, inferInstance, SubmersivePresentation.ofBijectiveAlgebraMap h,
    Presentation.ofBijectiveAlgebraMap_dimension h⟩

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