English
A specialized compatibility result: the equality of maps holds after transporting along algebra maps and equivalences.
Русский
Специализированный результат совместимости: равенство отображений сохраняется после переноса по алгебраическим отображениям и эквивалентностям.
LaTeX
$$$(\text{algEquiv } N S_n S_n') \circ (\text{algebraMap } R_m S_n)(x) = (\text{algebraMap } R_m' S_n') \circ (\text{algEquiv } M R_m R_m')(x)$$$
Lean4
/-- The localization of a singleton is a singleton. Cannot be an instance due to metavariables. -/
noncomputable def _root_.IsLocalization.unique (R Rₘ) [CommSemiring R] [CommSemiring Rₘ] (M : Submonoid R)
[Subsingleton R] [Algebra R Rₘ] [IsLocalization M Rₘ] : Unique Rₘ :=
have : Inhabited Rₘ := ⟨1⟩
(algEquiv M Rₘ).symm.injective.unique
