Theorems · Theorem · group theory
add_notMem_of_exponent_two
∀ {G : Type u} [inst : AddGroup G], AddMonoid.exponent G = 2 → ∀ {x y : G}, x ≠ 0 → y ≠ 0 → x ≠ y → x + y ∉ {x, y, 0}- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddMonoid.exponentstatement and proof · cited by 70
- AddMonoid.exponent_nsmul_eq_zeroproof · cited by 12
- addOrderOf_eq_primeproof · cited by 2
- add_notMem_of_addOrderOf_eq_twoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsAddKleinFour.eq_finset_univproof · cited by 1