Theorems · Theorem · group theory
add_neg_eq_zero
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a + -b = 0 ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- neg_negproof · cited by 960
- add_eq_zero_iff_eq_negproof · cited by 49
Cited by20
Results whose statement or proof uses this declaration.
- injective_iff_map_eq_zeroproof · cited by 62
- intervalIntegral.integral_add_adjacent_intervalsproof · cited by 15
- zsmul_eq_zsmul_iff_modEqproof · cited by 4
- AddSubgroup.upperCentralSeries_oneproof · cited by 4
- addCommutatorElement_eq_zero_iff_add_commproof · cited by 3
- AddSubgroup.disjoint_iff_add_eq_zeroproof · cited by 2
- AddSubgroup.lowerCentralSeries_succ_eq_botproof · cited by 2
- addConj_eq_zero_iffproof · cited by 1
- AddMonoidHom.liftOfRightInverseAux_comp_applyproof · cited by 1
- Set.injOn_iff_map_eq_zeroproof · cited by 1
- AlgebraicTopology.DoldKan.σ_comp_P_eq_zeroproof · cited by 1