instIsScalarTower — Mathlib

English

If there are scalar actions of R on M and of R1 on M with IsScalarTower, then C(α, M) carries an IsScalarTower structure with C(α, M) acting compatibly.

Русский

При существовании действия скаляра Z на M и R1 на M с условиями IsScalarTower, C(α, M) наследует структуру IsScalarTower.

LaTeX

$$$ IsScalarTower R R1 C(\alpha, M). $$$

Lean4

instance [SMul R M] [ContinuousConstSMul R M] [SMul R₁ M] [ContinuousConstSMul R₁ M] [SMul R R₁]
    [IsScalarTower R R₁ M] : IsScalarTower R R₁ C(α, M) where smul_assoc _ _ _ := ext fun _ => smul_assoc _ _ _

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