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Theorems · Theorem · group theory

Set.mem_pow

∀ {α : Type u_1} [inst : Monoid α] {s : Set α} {a : α} {n : ℕ}, a ∈ s ^ n ↔ ∃ f, (List.ofFn fun i => ↑(f i)).prod = a
Defined in
Mathlib.Algebra.Group.Pointwise.Set.ListOfFn
Cited by
3 results in Mathlib
Foundations
Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Monoid
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Around this declaration

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

ExteriorAlgebra.ιMulti_span_fixedDegree · cited by 3ExteriorAlgebra.ιMulti_sp…exteriorPower.ιMulti_span_fixedDegree_of_span_eq_top · cited by 2exteriorPower.ιMulti_span…ExteriorAlgebra.ιMulti_range · cited by 2ExteriorAlgebra.ιMulti_ra…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemMonoid · cited by 3887MonoidSet.NPow · cited by 51Set.NPowList.prod_replicate · cited by 29List.prod_replicateList.ofFn_const · cited by 13List.ofFn_constSet.mem_prod_list_ofFn · cited by 2Set.mem_prod_list_ofFnSet.mem_powCITED BYCITES

Cites7

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

Cited by3

Results whose statement or proof uses this declaration.