Theorems · Theorem · group theory
Set.zsmul_eq_empty
∀ {α : Type u_2} [inst : SubtractionMonoid α] {s : Set α} {n : ℤ}, n • s = ∅ ↔ s = ∅ ∧ n ≠ 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubtractionMonoid
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptyproof · cited by 2,627
- SubtractionMonoidstatement and proof · cited by 208
- zero_nsmulproof · cited by 137
- Set.nonempty_iff_ne_emptyproof · cited by 96
- ofNat_zsmulproof · cited by 24
- Set.ZSMulstatement · cited by 5
- Set.zero_nonemptyproof · cited by 3
- Set.Nonempty.zsmulproof · cited by 1
- Set.zsmul_emptyproof · cited by 1
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