insepDegree_eq_of_isSeparable — Mathlib

English

The q-power map on a basis preserves its nature as a basis in separable extensions.

Русский

Картографирование через q-пусть сохраняет характер базиса в разделяемых расширениях.

LaTeX

$$$\text{basis}_q^n$ is a basis$$

Lean4

/-- If `K / E / F` is a field extension tower, such that `E / F` is separable,
then $[K:F]_i = [K:E]_i$.
It is a special case of `Field.lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic`, and is an
intermediate result used to prove it. -/
theorem insepDegree_eq_of_isSeparable [Algebra.IsSeparable F E] : insepDegree F K = insepDegree E K :=
  by
  rw [insepDegree, insepDegree, separableClosure.eq_restrictScalars_of_isSeparable F E K]
  rfl

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