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Theorems · Theorem · group theory

Set.subset_pow

∀ {α : Type u_2} [inst : Monoid α] {s : Set α} {n : ℕ}, 1 ∈ s → n ≠ 0 → s ⊆ s ^ n
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 59 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.

Subgroup.closure_pow · cited by 1Subgroup.closure_powSubmonoid.closure_pow · cited by 0Submonoid.closure_powSet · cited by 53352SetMonoid · cited by 3887Monoidpow_one · cited by 894pow_oneSet.NPow · cited by 51Set.NPowSet.pow_subset_pow_right · cited by 2Set.pow_subset_pow_rightSet.subset_powCITED BYCITES

Cites5

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.