isTranscendenceBasis_iff — Mathlib

English

For any AlgEquiv e, IsTranscendenceBasis R (e ∘ x) iff IsTranscendenceBasis R x.

Русский

Для любого эквивалента Alb e: IsTranscendenceBasis R (e ∘ x) эквивалентно IsTranscendenceBasis R x.

LaTeX

$$$\\mathrm{IsTB}_R(e \\circ x) \\iff \\mathrm{IsTB}_R(x)$$$

Lean4

theorem isTranscendenceBasis_iff (e : A ≃ₐ[R] A') : IsTranscendenceBasis R (e ∘ x) ↔ IsTranscendenceBasis R x :=
  ⟨fun hx ↦ by convert e.symm.isTranscendenceBasis hx; ext; simp, e.isTranscendenceBasis⟩

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