Theorems · Theorem · group theory
Set.nsmul_empty
∀ {α : Type u_2} [inst : AddMonoid α] {n : ℕ}, n ≠ 0 → n • ∅ = ∅- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddMonoidstatement and proof · cited by 2,864
- succ_nsmulproof · cited by 65
- Set.NSMulstatement · cited by 42
- Set.add_emptyproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Set.nsmul_eq_emptyproof · cited by 2
- Set.zsmul_emptyproof · cited by 1
- AddGroup.card_nsmul_eq_card_nsmul_card_univproof · cited by 0