Theorems · Theorem · group theory
self_eq_neg
∀ {G : Type u_2} [inst : AddGroup G] [IsAddTorsionFree G] {a : G}, a = -a ↔ a = 0- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 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.
Cites5
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
- two_nsmulproof · cited by 67
- add_eq_zero_iff_eq_negproof · cited by 49
- two_nsmul_eq_zeroproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- neg_eq_selfproof · cited by 3
- ne_neg_of_mem_sphereproof · cited by 1
- MeasureTheory.integral_eq_zero_of_add_right_eq_negproof · cited by 1
- self_ne_negproof · cited by 0
- MeasureTheory.integral_eq_zero_of_add_left_eq_negproof · cited by 0