Theorems · Theorem · group theory
Submonoid.powers_eq_closure
∀ {M : Type u_1} [inst : Monoid M] (n : M), Submonoid.powers n = Submonoid.closure {n}- Cited by
- 6 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Submonoid.powersstatement · cited by 408
- Submonoid.closurestatement · cited by 167
- Submonoid.extproof · cited by 48
- Submonoid.mem_closure_singletonproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Submonoid.powers_leproof · cited by 19
- Submonoid.map_powersproof · cited by 10
- Algebra.FiniteType.of_span_eq_top_targetproof · cited by 2
- IsAlmostIntegral.isIntegral_of_nonZeroDivisors_le_comapproof · cited by 1
- Subgroup.toSubmonoid_zpowersproof · cited by 1
- Submonoid.powers_fgproof · cited by 0