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Theorems · Theorem · group theory

Finset.Nonempty.zsmul

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SubtractionMonoid α] {s : Finset α},
  s.Nonempty → ∀ {n : ℤ}, (n • s).Nonempty
Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqSubtractionMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.zsmul_eq_empty · cited by 0Finset.zsmul_eq_emptyFinset · cited by 13712FinsetFinset.Nonempty · cited by 1001Finset.NonemptySubtractionMonoid · cited by 208SubtractionMonoidnegSucc_zsmul · cited by 45negSucc_zsmulFinset.zsmul · cited by 6Finset.zsmulFinset.neg_nonempty_iff · cited by 4Finset.neg_nonempty_iffFinset.Nonempty.nsmul · cited by 2Nonempty.nsmulNonempty.zsmulCITED BYCITES

Cites7

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Cited by1

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