Theorems · Theorem · group theory
AddCommute.addCommutator_eq
∀ {G : Type u_1} [inst : AddGroup G] {g₁ g₂ : G}, AddCommute g₁ g₂ → ⁅g₁, g₂⁆ = 0- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 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 and proof · cited by 185
- addCommutatorElementstatement · cited by 35
- addCommutatorElement_eq_zero_iff_addCommuteproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- addCommutatorElement_selfproof · cited by 1
- addCommutatorElement_zero_leftproof · cited by 1
- addCommutatorElement_zero_rightproof · cited by 0