Theorems · Theorem · group theory
mod_addOrderOf_nsmul
∀ {G : Type u_1} [inst : AddMonoid G] (x : G) (n : ℕ), (n % addOrderOf x) • x = n • x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 24 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.
Cites7
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
- addOrderOfstatement and proof · cited by 208
- nsmul_zeroproof · cited by 73
- add_nsmulproof · cited by 44
- mul_nsmulproof · cited by 24
- addOrderOf_nsmul_eq_zeroproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- finEquivMultiples_symm_applyproof · cited by 2
- IsOfFinAddOrder.mem_multiples_iff_mem_range_addOrderOfproof · cited by 2
- mod_natCard_nsmulproof · cited by 1
- exists_nsmul_eq_self_of_coprimeproof · cited by 0
- mod_card_nsmulproof · cited by 0
- mem_multiples_iff_mem_range_addOrderOfproof · cited by 0