Theorems · Theorem · group theory
AddCommute.addOrderOf_dvd_lcm_add
∀ {G : Type u_1} [inst : AddMonoid G] {x y : G}, AddCommute x y → addOrderOf y ∣ (addOrderOf x).lcm (addOrderOf (x + y))- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- addOrderOfstatement and proof · cited by 208
- AddCommutestatement and proof · cited by 185
- Dvd.dvd.transproof · cited by 148
- succ_nsmulproof · cited by 65
- dvd_zeroproof · cited by 63
- AddCommute.reflproof · cited by 12
- addOrderOf_nsmul_eq_zeroproof · cited by 11
- AddCommute.add_rightproof · cited by 4
- AddCommute.nsmul_leftproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.addOrderOf_add_eq_right_of_forall_prime_mul_dvdproof · cited by 2