Theorems · Theorem · group theory
Submonoid.pow_mem
∀ {M : Type u_5} [inst : Monoid M] (S : Submonoid M) {x : M}, x ∈ S → ∀ (n : ℕ), x ^ n ∈ S- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by6
Results whose statement or proof uses this declaration.
- associatedPrimes.subset_union_of_exactproof · cited by 2
- IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zeroproof · cited by 2
- Commute.isNilpotent_mul_left_iffproof · cited by 1
- IsGroupLikeElem.powproof · cited by 0
- Commute.isNilpotent_mul_right_iffproof · cited by 0
- AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrimeproof · cited by 0