Theorems · Theorem · group theory
neg_eq_self
∀ {G : Type u_2} [inst : AddGroup G] [IsAddTorsionFree G] {a : G}, -a = a ↔ a = 0- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddTorsionFree
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.
- AddGroupstatement and proof · cited by 4,410
- IsAddTorsionFreestatement and proof · cited by 155
- self_eq_negproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Circle.neg_ne_selfproof · cited by 1
- Function.zero_of_even_and_oddproof · cited by 0
- neg_ne_selfproof · cited by 0