Theorems · Theorem · group theory
ofNat_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (a : G) (n : ℕ), OfNat.ofNat n • a = OfNat.ofNat n • a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- SubNegMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- natCast_zsmulproof · cited by 118
- SubNegMonoidstatement and proof · cited by 79
Cited by24
Results whose statement or proof uses this declaration.
- one_zsmulproof · cited by 59
- neg_zsmulproof · cited by 41
- two_zsmulproof · cited by 21
- add_zsmulproof · cited by 21
- add_one_zsmulproof · cited by 19
- AddSubgroup.zmultiples_eq_zmultiples_iffproof · cited by 3
- injective_zsmul_iff_not_isOfFinAddOrderproof · cited by 2
- AddSubgroup.exists_finsupp_of_mem_closure_rangeproof · cited by 2
- Finset.subset_addSpanproof · cited by 1
- Finset.sum_sub_sum_mem_addSpanproof · cited by 1
- not_isAddCyclic_of_denselyOrderedproof · cited by 1
- Finset.small_nsmul_of_small_triplingproof · cited by 1