Theorems · Theorem · group theory
AddCommute.of_addOrderOf_dvd_two
∀ {G : Type u} [inst : AddMonoid G] [IsCancelAdd G], (∀ (g : G), addOrderOf g ∣ 2) → ∀ (a b : G), AddCommute a b- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidIsCancelAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- add_zeroproof · cited by 2,707
- add_assocproof · cited by 746
- addOrderOfstatement and proof · cited by 208
- AddCommutestatement · cited by 185
- IsCancelAddstatement and proof · cited by 79
- add_right_injproof · cited by 71
- two_nsmulproof · cited by 67
- add_left_injproof · cited by 36
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- addCommute_iff_eqproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- add_comm_of_exponent_twoproof · cited by 1