Theorems · Theorem · group theory
IsOfFinAddOrder.nsmul_eq_nsmul_iff_modEq
∀ {G : Type u_1} [inst : AddMonoid G] {x : G} {n m : ℕ}, IsOfFinAddOrder x → (n • x = m • x ↔ n ≡ m [MOD addOrderOf x])- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 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.
Cites13
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
- Nat.ModEqstatement and proof · cited by 225
- addOrderOfstatement and proof · cited by 208
- IsOfFinAddOrderstatement and proof · cited by 105
- le_of_not_geproof · cited by 72
- add_nsmulproof · cited by 44
- Nat.ModEq.commproof · cited by 11
- Nat.ModEq.add_left_cancel'proof · cited by 7
- Nat.ModEq.add_leftproof · cited by 6
- IsAddUnit.nsmulproof · cited by 4
- nsmul_eq_zero_iff_modEqproof · cited by 3
- IsAddUnit.add_eq_leftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsOfFinAddOrder.nsmul_inj_modproof · cited by 0