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Theorems · Theorem · group theory

Set.Nonempty.nsmul

∀ {α : Type u_2} [inst : AddMonoid α] {s : Set α}, s.Nonempty → ∀ {n : ℕ}, (n • s).Nonempty
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoid
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Around this declaration

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

Set.nsmul_eq_empty · cited by 2Set.nsmul_eq_emptySet.Nonempty.zsmul · cited by 1Nonempty.zsmulSet · cited by 53352SetAddMonoid · cited by 2864AddMonoidSet.Nonempty · cited by 2627Set.NonemptySet.addMonoid · cited by 18Set.addMonoidNonempty.nsmulCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.