Mathlib Map

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 * a

In 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.

Cited by2

Results whose statement or proof uses this declaration.