Theorems · Theorem · group theory
Submonoid.mem_powers
∀ {M : Type u_1} [inst : Monoid M] (n : M), n ∈ Submonoid.powers n- Cited by
- 13 results in Mathlib
- Foundations
- Depth 25 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- pow_oneproof · cited by 894
- Submonoid.powersstatement · cited by 408
Cited by13
Results whose statement or proof uses this declaration.
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
- exists_bijective_map_powersproof · cited by 3
- IsLocalization.isMaximal_iff_isMaximal_disjointproof · cited by 3
- Ideal.disjoint_powers_iff_notMemproof · cited by 2
- LocalizedModule.exists_subsingleton_awayproof · cited by 2
- isJacobsonRing_localizationproof · cited by 1
- Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModuleproof · cited by 1
- Monoid.finite_set_isOfFiniteOrder_of_descentproof · cited by 1
- Ideal.exists_le_prime_notMem_of_isIdempotentElemproof · cited by 1
- PrimeSpectrum.isLocalization_away_iff_atPrime_of_basicOpen_eq_singletonproof · cited by 1
- IsIdempotentElem.coe_powersproof · cited by 1
- IsLocalization.away_of_isIdempotentElem_of_mulproof · cited by 1