Theorems · Theorem · group theory
neg_eq_self_of_addOrderOf_eq_two
∀ {G : Type u} [inst : AddGroup G] {x : G}, addOrderOf x = 2 → -x = x- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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
- addOrderOfstatement and proof · cited by 208
- two_nsmulproof · cited by 67
- addOrderOf_nsmul_eq_zeroproof · cited by 11
- neg_eq_of_add_eq_zero_leftproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- add_notMem_of_addOrderOf_eq_twoproof · cited by 1