Theorems · Theorem · group theory
Submonoid.powers_le
∀ {M : Type u_1} [inst : Monoid M] {n : M} {P : Submonoid M}, Submonoid.powers n ≤ P ↔ n ∈ P- Cited by
- 19 results in Mathlib
- Foundations
- Depth 68 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 and proof · cited by 3,086
- Submonoid.powersstatement · cited by 408
- Submonoid.powers_eq_closureproof · cited by 6
Cited by19
Results whose statement or proof uses this declaration.
- Submonoid.powers_oneproof · cited by 7
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eqproof · cited by 3
- AlgebraicGeometry.Proj.awayMap_awayToSectionproof · cited by 2
- Module.FinitePresentation.exists_free_localizedModule_powersproof · cited by 2
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalkstatement and proof · cited by 2
- Module.FinitePresentation.exists_basis_localizedModule_powersstatement and proof · cited by 1
- Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModulestatement and proof · cited by 1
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_applystatement and proof · cited by 1
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germstatement · cited by 1
- PrimeSpectrum.isLocalization_away_iff_atPrime_of_basicOpen_eq_singletonproof · cited by 1
- IsAlmostIntegral.isIntegral_of_nonZeroDivisors_le_comapproof · cited by 1
- IsIdempotentElem.coe_powersproof · cited by 1