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Theorems · Theorem · group theory

Set.pow_mem_pow

∀ {α : Type u_2} [inst : Monoid α] {s : Set α} {a : α} {n : ℕ}, a ∈ s → a ^ n ∈ s ^ n
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 58 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.

Submodule.pow_mem_pow · cited by 3Submodule.pow_mem_powSet.one_mem_pow · cited by 1Set.one_mem_powSet · cited by 53352SetMonoid · cited by 3887MonoidSet.singleton_subset_iff · cited by 206Set.singleton_subset_iffSet.NPow · cited by 51Set.NPowSet.pow_subset_pow_left · cited by 2Set.pow_subset_pow_leftSet.singleton_pow · cited by 2Set.singleton_powSet.pow_mem_powCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.