of_tower — Mathlib

English

If K and L are number fields and E is a type with field structure and IsScalarTower K E L, then E is a number field.

Русский

Если K и L — числа поля, и E удовлетворяет требованию IsScalarTower K E L, то E — число поле.

LaTeX

$$$$ NumberField(E) $$$$

Lean4

theorem of_tower [NumberField K] [NumberField L] [Algebra K L] (E : Type*) [Field E] [Algebra K E] [Algebra E L]
    [IsScalarTower K E L] : NumberField E :=
  letI := Module.Finite.left K E L
  of_module_finite K E

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