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Theorems · Theorem · group theory

Set.mul_mem_center

∀ {M : Type u_1} [inst : Mul M] {z₁ z₂ : M}, z₁ ∈ Set.center M → z₂ ∈ Set.center M → z₁ * z₂ ∈ Set.center M
Defined in
Mathlib.Algebra.Group.Center
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Mul
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Around this declaration

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

Subsemigroup.center · cited by 38Subsemigroup.centerSet.div_mem_center · cited by 0Set.div_mem_centerSet · cited by 53352SetSet.center · cited by 49Set.centerSet.mul_mem_centerCITED BYCITES

Cites2

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

  • Setstatement · cited by 53,352
  • Set.centerstatement and proof · cited by 49

Cited by2

Results whose statement or proof uses this declaration.