Theorems · Theorem · group theory
negSucc_zsmul
∀ {G : Type u_2} [inst : SubNegMonoid G] (a : G) (n : ℕ), Int.negSucc n • a = -((n + 1) • a)- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 45 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.
Cites3
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
- SubNegMonoid.zsmul_neg'proof · cited by 2
Cited by45
Results whose statement or proof uses this declaration.
- zsmul_eq_mulproof · cited by 120
- neg_zsmulproof · cited by 41
- Int.cast_smul_eq_zsmulproof · cited by 28
- zsmul_oneproof · cited by 26
- add_one_zsmulproof · cited by 19
- mul_zsmul'proof · cited by 16
- neg_one_zsmulproof · cited by 14
- zsmul_memproof · cited by 14
- zsmul_zeroproof · cited by 14
- Function.Periodic.zsmulproof · cited by 9
- zsmul_negproof · cited by 6
- AddConstMapClass.map_add_zsmulproof · cited by 5