instSMulMemClass — Mathlib

English

The action of R on A induces a SMulMemClass structure on Subalgebra R A, so that r • x ∈ S whenever x ∈ S and r ∈ R.

Русский

Действие R на A порождает структуру SMulMemClass на Subalgebra R A; если x ∈ S и r ∈ R, то r • x ∈ S.

LaTeX

$$$\\text{SMulMemClass}(\\mathrm{Subalgebra}\\; R\\; A)$ with $\\mathrm{smul\_mem}(r,x,hx)$.$$

Lean4

instance instSMulMemClass : SMulMemClass (Subalgebra R A) R A where
  smul_mem {S} r x hx := (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem' r) hx

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