isIntegral_gen — Mathlib

English

For a generator α, IsIntegral F AdjoinSimple.gen F α is equivalent to IsIntegral F α.

Русский

Для генератора α семантика IsIntegral F AdjoinSimple.gen F α равна IsIntegral F α.

LaTeX

$$IsIntegral F (AdjoinSimple.gen F α) ⇔ IsIntegral F α$$

Lean4

@[simp]
theorem isIntegral_gen : IsIntegral F (AdjoinSimple.gen F α) ↔ IsIntegral F α :=
  by
  conv_rhs => rw [← AdjoinSimple.algebraMap_gen F α]
  rw [isIntegral_algebraMap_iff (algebraMap F⟮α⟯ E).injective]

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