Theorems · Theorem · group theory
zsmul_zero
∀ {α : Type u_1} [inst : SubtractionMonoid α] (n : ℤ), n • 0 = 0- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_zeroproof · cited by 542
- SubtractionMonoidstatement and proof · cited by 208
- natCast_zsmulproof · cited by 118
- nsmul_zeroproof · cited by 73
- negSucc_zsmulproof · cited by 45
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroproof · cited by 3
- mod_addOrderOf_zsmulproof · cited by 3
- gcd_nsmul_eq_zeroproof · cited by 3
- zmodAddEquivOfGenerator_apply_intCastproof · cited by 3
- Real.Angle.cos_eq_iff_coe_eq_or_eq_negproof · cited by 3
- zsmul_smul_addOrderOfproof · cited by 2
- AddSubgroup.closure_singleton_zeroproof · cited by 2
- Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iffproof · cited by 2
- Function.HasFiniteSupport.zsmulproof · cited by 1
- not_isAddCyclic_of_denselyOrderedproof · cited by 1
- AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInftyproof · cited by 1