Theorems · Theorem · group theory
add_eq_zero_iff_eq_neg
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 ↔ a = -b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 12 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_add_cancelproof · cited by 256
- eq_neg_of_add_eq_zero_leftproof · cited by 21
Cited by49
Results whose statement or proof uses this declaration.
- eq_neg_iff_add_eq_zeroproof · cited by 32
- add_neg_eq_zeroproof · cited by 20
- neg_add_eq_zeroproof · cited by 14
- add_eq_zero_iff_neg_eqproof · cited by 11
- IsAlgClosed.algebraMap_bijective_of_isIntegralproof · cited by 6
- ZLattice.rankproof · cited by 5
- integral_cpowproof · cited by 5
- Complex.cos_eq_zero_iffproof · cited by 5
- self_eq_negproof · cited by 5
- iSupIndep.dfinsupp_lsum_injectiveproof · cited by 5
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_componentproof · cited by 3