ofBijectiveAlgebraMap — Mathlib

English

If the algebra map from R to S is bijective, the empty generators yield a pre-submersive presentation with no relations.

Русский

Если алгебраическая карта R → S биективна, пустые генераторы дают пред-submersивное представление без отношений.

LaTeX

$$ofBijectiveAlgebraMap(h) : PreSubmersivePresentation R S PEmpty PEmpty$$

Lean4

/-- If `algebraMap R S` is bijective, the empty generators are a pre-submersive
presentation with no relations. -/
noncomputable def ofBijectiveAlgebraMap (h : Function.Bijective (algebraMap R S)) :
    PreSubmersivePresentation R S PEmpty.{w + 1} PEmpty.{t + 1}
    where
  toPresentation := Presentation.ofBijectiveAlgebraMap.{t, w} h
  map := PEmpty.elim
  map_inj (a b : PEmpty) h := by contradiction

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