Theorems · Theorem · group theory
addCommutatorElement_eq_zero_iff_add_comm
∀ {G : Type u_1} [inst : AddGroup G] {g₁ g₂ : G}, ⁅g₁, g₂⁆ = 0 ↔ g₁ + g₂ = g₂ + g₁- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- addCommutatorElementstatement · cited by 35
- add_neg_eq_zeroproof · cited by 20
- add_neg_eq_iff_eq_addproof · cited by 12
- addCommutatorElement_defproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.addCommutator_eq_bot_iff_le_centralizerproof · cited by 7
- addCommutatorElement_eq_zero_iff_addCommuteproof · cited by 1
- AddSubgroup.Normal.quotient_commutative_iff_addCommutator_leproof · cited by 1