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Theorems · Theorem · group theory

Set.Nonempty.pow

∀ {α : Type u_2} [inst : Monoid α] {s : Set α}, s.Nonempty → ∀ {n : ℕ}, (s ^ n).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
Monoid
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Around this declaration

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

Set.Nonempty.zpow · cited by 1Nonempty.zpowSet.pow_eq_empty · cited by 0Set.pow_eq_emptySet · cited by 53352SetMonoid · cited by 3887MonoidSet.Nonempty · cited by 2627Set.NonemptySet.monoid · cited by 19Set.monoidNonempty.powCITED BYCITES

Cites4

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

  • Setstatement and proof · cited by 53,352
  • Monoidstatement and proof · cited by 3,887
  • Set.Nonemptystatement and proof · cited by 2,627
  • Set.monoidstatement · cited by 19

Cited by2

Results whose statement or proof uses this declaration.