Theorems · Theorem · group theory
natCast_zsmul
∀ {G : Type u_1} [inst : SubNegMonoid G] (a : G) (n : ℕ), ↑n • a = n • a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 64 definitions · uses no axioms
- Assumes
- SubNegMonoid
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.
- SubNegMonoidstatement and proof · cited by 79
Cited by118
Results whose statement or proof uses this declaration.
- zsmul_eq_mulproof · cited by 120
- negSucc_zsmulproof · cited by 45
- neg_zsmulproof · cited by 41
- zsmul_oneproof · cited by 26
- ofNat_zsmulproof · cited by 24
- add_one_zsmulproof · cited by 19
- mul_zsmul'proof · cited by 16
- zsmul_memproof · cited by 14
- zsmul_zeroproof · cited by 14
- Function.Periodic.zsmulproof · cited by 9
- RootPairing.root_add_nsmul_mem_range_iff_le_chainTopCoeffproof · cited by 7
- RootPairing.Base.exists_root_eq_sum_intproof · cited by 7