Theorems · Theorem · group theory
addCommutatorElement_eq_zero_iff_addCommute
∀ {G : Type u_1} [inst : AddGroup G] {g₁ g₂ : G}, ⁅g₁, g₂⁆ = 0 ↔ AddCommute g₁ g₂- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Bracket.bracketstatement · cited by 642
- AddCommutestatement · cited by 185
- addCommutatorElementstatement · cited by 35
- addCommutatorElement_eq_zero_iff_add_commproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.addCommutator_eqproof · cited by 3