restrictScalars_top — Mathlib

English

Restricting scalars preserves the top subalgebra: restricting the top S-subalgebra of A to R yields the top R-subalgebra of A.

Русский

Ограничение скаляров сохраняет максимум: ограничение топ-subалгебры S на R даёт верхнюю подалгебру над A.

LaTeX

$$$\restrictScalars R (\top_{S}) = \top_{R}$$$

Lean4

@[simp]
theorem restrictScalars_top : restrictScalars R (⊤ : Subalgebra S A) = ⊤ :=
  -- Porting note: `by dsimp` used to be `rfl`. This appears to work but causes
    -- this theorem to timeout in the kernel after minutes of thinking.

  SetLike.coe_injective <| by dsimp

Похожие утверждения