Theorems · Theorem · group theory
succ_nsmul
∀ {M : Type u_2} [inst : AddMonoid M] (a : M) (n : ℕ), (n + 1) • a = n • a + a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- AddMonoid.nsmul_succproof · cited by 1
Cited by65
Results whose statement or proof uses this declaration.
- nsmul_eq_mulproof · cited by 369
- two_nsmulproof · cited by 67
- one_nsmulproof · cited by 63
- add_one_zsmulproof · cited by 19
- Multiset.count_nsmulproof · cited by 10
- Finset.coe_nsmulproof · cited by 9
- nsmul_eq_mul'proof · cited by 8
- AddSemiconjBy.nsmul_rightproof · cited by 5
- HahnSeries.single_powproof · cited by 5
- nsmul_left_strictMonoproof · cited by 4
- Finset.nsmul_emptyproof · cited by 4
- Set.nsmul_emptyproof · cited by 3