lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left

English

A variant of the above with Right in the lifting identity; the equality holds in the symmetric setting.

Русский

Вариант той же идеи с правой стороны тильда; тождество сохраняется в симметричном виде.

LaTeX

$$$\operatorname{lift}_{F}(\operatorname{rank}) \cdot \operatorname{lift}_{E}(\operatorname{rank}) = \operatorname{rank}_{A}(E)$$$

Lean4

theorem lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left (H : A.LinearDisjoint L) [Algebra.IsAlgebraic F A] :
    Cardinal.lift.{v} (Module.rank F L) * Cardinal.lift.{w} (Module.rank (adjoin L (A : Set E)) E) =
      Cardinal.lift.{w} (Module.rank A E) :=
  H.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic (.inl ‹_›)

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