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Theorems · Theorem · group theory

Set.mem_nsmul

∀ {α : Type u_1} [inst : AddMonoid α] {s : Set α} {a : α} {n : ℕ}, a ∈ n • s ↔ ∃ f, (List.ofFn fun i => ↑(f i)).sum = a
Defined in
Mathlib.Algebra.Group.Pointwise.Set.ListOfFn
Cited by
1 results in Mathlib
Foundations
Depth 49 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.

Finset.mem_nsmul · cited by 0Finset.mem_nsmulSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemAddMonoid · cited by 2864AddMonoidSet.NSMul · cited by 42Set.NSMulList.sum_replicate · cited by 19List.sum_replicateList.ofFn_const · cited by 13List.ofFn_constSet.mem_sum_list_ofFn · cited by 3Set.mem_sum_list_ofFnSet.mem_nsmulCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.