Theorems · Theorem · group theory
eq_neg_iff_add_eq_zero
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a = -b ↔ a + b = 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 32 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.
Cites2
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
- add_eq_zero_iff_eq_negproof · cited by 49
Cited by32
Results whose statement or proof uses this declaration.
- CharZero.eq_neg_self_iffproof · cited by 6
- padicValRat.invproof · cited by 5
- RootPairing.pairing_smul_root_eq_of_not_linearIndependentproof · cited by 3
- linearIndependent_sumproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- Complex.exp_eq_one_iffproof · cited by 3
- minpoly.mem_range_of_degree_eq_oneproof · cited by 3
- Real.Angle.cos_eq_iff_coe_eq_or_eq_negproof · cited by 3
- Polynomial.eval₂_negproof · cited by 3
- neg_one_pow_expChar_powproof · cited by 2
- CircleDeg1Lift.translationNumber_units_invproof · cited by 2
- AddSubgroup.disjoint_iff_add_eq_zeroproof · cited by 2