Theorems · Theorem · group theory
Finset.zsmul_empty
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SubtractionMonoid α] {n : ℤ}, n ≠ 0 → n • ∅ = ∅- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqSubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- one_ne_zeroproof · cited by 885
- SubtractionMonoidstatement and proof · cited by 208
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- Finset.zsmulstatement · cited by 6
- Finset.nsmul_emptyproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Finset.zsmul_eq_emptyproof · cited by 0
- Finset.small_alternating_nsmul_of_small_triplingproof · cited by 0