Theorems · Theorem · group theory
Subsemigroup.centralizer_eq_top_iff_subset
∀ {M : Type u_1} [inst : Semigroup M] {s : Set M}, Subsemigroup.centralizer s = ⊤ ↔ s ⊆ ↑(Subsemigroup.center M)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semigroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement · cited by 9,680
- SetLike.coestatement · cited by 8,199
- Subsemigroupstatement · cited by 323
- Semigroupstatement and proof · cited by 202
- SetLike.ext'_iffproof · cited by 78
- Subsemigroup.centerstatement · cited by 38
- Subsemigroup.centralizerstatement · cited by 10
- Set.centralizer_eq_top_iff_subsetproof · cited by 8
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