smulCommClass_symm_self — Mathlib

English

If the coefficient ring k is commutative in its own sense, then the smul-commutativity extends in a symmetric way to MonoidAlgebra.

Русский

Если коэффициентовый кольцо k коммутативно внутри себя, то справедливо симметричное smul‑commutativity для MonoidAlgebra.

LaTeX

$$$$\text{SMulCommClass } R k[G] k[G]$$$$

Lean4

instance smulCommClass_symm_self [SMulCommClass k R k] : SMulCommClass (MonoidAlgebra k G) R (MonoidAlgebra k G) :=
  ⟨fun t a b => by
    haveI := SMulCommClass.symm k R k
    rw [← smul_comm]⟩

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