Theorems · Theorem · group theory
mul_notMem_of_orderOf_eq_two
∀ {G : Type u} [inst : Group G] {x y : G}, orderOf x = 2 → orderOf y = 2 → x ≠ y → x * y ∉ {x, y, 1}- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- orderOfstatement and proof · cited by 324
- orderOf_oneproof · cited by 15
- inv_eq_self_of_orderOf_eq_twoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- mul_notMem_of_exponent_twoproof · cited by 1