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