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Theorems · Theorem · group theory

Set.center_subset_centralizer

∀ {M : Type u_1} [inst : Mul M] (S : Set M), Set.center M ⊆ S.centralizer
Defined in
Mathlib.Algebra.Group.Center
Cited by
8 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.center_le_centralizer · cited by 1Subgroup.center_le_centra…Subalgebra.center_le_centralizer · cited by 0Subalgebra.center_le_cent…Subsemigroup.center_le_centralizer · cited by 0Subsemigroup.center_le_ce…NonUnitalSubring.center_le_centralizer · cited by 0NonUnitalSubring.center_l…Subring.center_le_centralizer · cited by 0Subring.center_le_central…Submonoid.center_le_centralizer · cited by 0Submonoid.center_le_centr…Subsemiring.center_le_centralizer · cited by 0Subsemiring.center_le_cen…NonUnitalSubsemiring.center_le_centralizer · cited by 0NonUnitalSubsemiring.cent…Set · cited by 53352SetCommute.symm · cited by 79Commute.symmSet.centralizer · cited by 57Set.centralizerSet.center · cited by 49Set.centerIsMulCentral.comm · cited by 26IsMulCentral.commSet.center_subset_centralizerCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.