Theorems · Theorem · group theory
eq_neg_of_add_eq_zero_right
∀ {α : Type u_1} [inst : SubtractionMonoid α] {a b : α}, a + b = 0 → b = -a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 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_rightproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- ascPochhammer_eval_eq_zero_iffproof · cited by 3
- Set.add_eq_zero_iffproof · cited by 3
- CategoryTheory.Adjunction.LeftAdjointCommShift.iso_hom_appproof · cited by 2
- Finset.centerMass_of_sum_add_sum_eq_zeroproof · cited by 1
- CategoryTheory.Adjunction.LeftAdjointCommShift.iso_inv_appproof · cited by 1
- jacobiSum_nontrivial_invproof · cited by 0
- vieta_formula_quadraticproof · cited by 0
- eq_zero_sub_of_add_eq_zero_rightproof · cited by 0