Theorems · Theorem · group theory
neg_eq_of_add_eq_zero_right
∀ {G : Type u_1} [inst : SubtractionMonoid G] {a b : G}, a + b = 0 → -a = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 6 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
- SubtractionMonoid.neg_eq_of_addproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- neg_vsub_eq_vsub_revproof · cited by 87
- eq_of_sub_eq_zeroproof · cited by 27
- eq_neg_of_add_eq_zero_rightproof · cited by 8
- AddUnits.val_neg_eq_neg_valproof · cited by 8
- neg_eq_of_add_eq_zero_leftproof · cited by 5
- CliffordAlgebra.EquivEven.neg_e0_mul_vproof · cited by 3
- Set.add_eq_zero_iffproof · cited by 3
- AddSubmonoid.leftNeg_eq_negproof · cited by 0
- AddSubgroup.leftTransversals.diff_negproof · cited by 0