Theorems · Theorem · group theory
mul_comm_of_exponent_two
∀ {G : Type u} [inst : Monoid G] [IsCancelMul G], Monoid.exponent G = 2 → ∀ (a b : G), a * b = b * aIn a cancellative monoid of exponent two, all elements commute.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsCancelMul
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.
- Monoidstatement and proof · cited by 3,887
- Monoid.exponentstatement and proof · cited by 128
- IsCancelMulstatement and proof · cited by 32
- Monoid.order_dvd_exponentproof · cited by 14
- Commute.of_orderOf_dvd_twoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- commMonoidOfExponentTwoproof · cited by 0
- IsKleinFour.isMulCommutativeproof · cited by 0