Theorems · Theorem · group theory
Submonoid.closure_singleton_eq
∀ {M : Type u_1} [inst : Monoid M] (x : M), Submonoid.closure {x} = MonoidHom.mrange ((powersHom M) x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- pow_oneproof · cited by 894
- Multiplicativestatement and proof · cited by 875
- Multiplicative.ofAddproof · cited by 237
- Set.singleton_subset_iffproof · cited by 206
- Set.mem_singletonproof · cited by 183
- Submonoid.closurestatement and proof · cited by 167
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.mem_closure_singletonproof · cited by 2