Theorems · Theorem · group theory
neg_eq_of_add_eq_zero_left
∀ {G : Type u_1} [inst : SubtractionMonoid G] {a b : G}, a + b = 0 → -b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 5 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_negproof · cited by 960
- SubtractionMonoidstatement and proof · cited by 208
- neg_eq_of_add_eq_zero_rightproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- eq_neg_of_add_eq_zero_leftproof · cited by 21
- CategoryTheory.shift_shiftFunctorCompIsoId_hom_appproof · cited by 5
- Set.add_eq_zero_iffproof · cited by 3
- neg_eq_self_of_addOrderOf_eq_twoproof · cited by 1
- neg_eq_self_of_exponent_twoproof · cited by 1