centralizer_centralizer_centralizer

English

If every pair of elements of S commutes, then the closure of S in M is a commutative monoid.

Русский

Если любой два элемента S commute, то замыкание S в M образует коммутативный моноид.

LaTeX

$$If all a,b ∈ S satisfy ab = ba, then closure(S) is a commutative monoid.$$

Lean4

@[to_additive (attr := simp)]
theorem centralizer_centralizer_centralizer {s : Set M} : centralizer s.centralizer.centralizer = centralizer s :=
  by
  apply SetLike.coe_injective
  simp only [coe_centralizer, Set.centralizer_centralizer_centralizer]

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