Theorems · Theorem · group theory
nsmul_zero
∀ {M : Type u_2} [inst : AddMonoid M] (n : ℕ), n • 0 = 0- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 73 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by73
Results whose statement or proof uses this declaration.
- Finset.sum_const_zeroproof · cited by 219
- Nat.factorization_powproof · cited by 17
- zsmul_zeroproof · cited by 14
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- ArchimedeanClass.mk_eq_top_iffproof · cited by 7
- not_isOfFinAddOrder_of_isAddTorsionFreeproof · cited by 7
- mod_addOrderOf_nsmulproof · cited by 7
- LieAlgebra.IsKilling.coroot_eq_zero_iffproof · cited by 6
- Polynomial.natDegree_multiset_prod_of_monicproof · cited by 4
- gcd_nsmul_eq_zeroproof · cited by 3
- AddMonoidHom.noncommPiCoprod_singleproof · cited by 3
- fwdDiff_iter_pow_eq_zero_of_ltproof · cited by 3