Theorems · Theorem · group theory
one_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (a : G), 1 • a = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SubNegMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SubNegMonoidstatement and proof · cited by 79
- one_nsmulproof · cited by 63
- ofNat_zsmulproof · cited by 24
Cited by59
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_zmultiplesproof · cited by 10
- AddSubgroup.mem_closure_singletonproof · cited by 6
- neg_one_zsmul_addproof · cited by 5
- one_add_zsmulproof · cited by 4
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- Function.Antiperiodic.add_zsmul_eqproof · cited by 3
- StrictConvexOn.map_sum_ltproof · cited by 3
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroproof · cited by 3
- AddSubgroup.zmultiples_eq_zmultiples_iffproof · cited by 3
- AddConstMapClass.rel_map_of_Iccproof · cited by 2
- toIocDiv_add_rightproof · cited by 2
- QuadraticMap.associated_toQuadraticMapproof · cited by 2