Theorems · Theorem · group theory
eq_neg_of_add_eq_zero_left
∀ {G : Type u_1} [inst : SubtractionMonoid G] {a b : G}, a + b = 0 → a = -b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- SubtractionMonoid
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.
- SubtractionMonoidstatement and proof · cited by 208
- neg_eq_of_add_eq_zero_leftproof · cited by 5
Cited by21
Results whose statement or proof uses this declaration.
- map_negproof · cited by 378
- neg_smulproof · cited by 306
- smul_negproof · cited by 181
- add_eq_zero_iff_eq_negproof · cited by 49
- Derivation.leibniz_of_mul_eq_oneproof · cited by 4
- Set.add_eq_zero_iffproof · cited by 3
- CliffordAlgebra.ι_mul_ι_comm_of_isOrthoproof · cited by 3
- AlternatingMap.map_swapproof · cited by 2
- MultilinearMap.map_update_negproof · cited by 2
- Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_memproof · cited by 2
- Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegreeproof · cited by 1
- eq_of_neg_add_eq_zeroproof · cited by 1