Theorems · Theorem · group theory
nsmul_eq_nsmul_iff_modEq
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] {x : G} {m n : ℕ}, n • x = m • x ↔ n ≡ m [MOD addOrderOf x]- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoid
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.
- add_zeroproof · cited by 2,707
- Nat.ModEqstatement and proof · cited by 225
- addOrderOfstatement and proof · cited by 208
- le_of_not_geproof · cited by 72
- add_nsmulproof · cited by 44
- AddLeftCancelMonoidstatement and proof · cited by 37
- add_left_cancel_iffproof · cited by 17
- Nat.ModEq.commproof · cited by 11
- Nat.ModEq.add_left_cancel'proof · cited by 7
- Nat.ModEq.add_leftproof · cited by 6
- nsmul_eq_zero_iff_modEqproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- injective_nsmul_iff_not_isOfFinAddOrderproof · cited by 1
- nsmul_inj_modproof · cited by 0
- IsAddCyclic.extproof · cited by 0
- nsmul_inj_iff_of_addOrderOf_eq_zeroproof · cited by 0