instSMulSubtypeMem — Mathlib

English

There is a canonical SMul action of S on α induced by the ambient algebra action, i.e., the action on a subtype is inherited from the ambient action.

Русский

Существует каноническое действие SMul Subtype mem S на α, индуцируемое действием над окружавшим алгебра-объектом.

LaTeX

$$$[SMul A \alpha] \Rightarrow SMul S \alpha$ via the inclusion.$$

Lean4

/-- The action by a subalgebra is the action by the underlying algebra. -/
instance [SMul A α] (S : Subalgebra R A) : SMul S α :=
  inferInstanceAs (SMul S.toSubsemiring α)

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