Theorems · Definition · group theory
Submonoid.closure
{M : Type u_1} → [inst : MulOneClass M] → Set M → Submonoid MThe Submonoid generated by a set.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 167 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 66 definitions · uses propext, Quot.sound
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- InfSet.sInfproof · cited by 935
Cited by175
Results whose statement or proof uses this declaration.
- Polynomial.Splitsproof · cited by 290
- Submonoid.subset_closurestatement · cited by 46
- Submonoid.closure_inductionstatement and proof · cited by 27
- Submonoid.closure_lestatement · cited by 27
- Submonoid.FGproof · cited by 24
- Polynomial.Splits.mapproof · cited by 19
- Submonoid.closure_eqstatement · cited by 13
- Algebra.adjoin_eq_spanstatement and proof · cited by 13
- MonoidHom.map_mclosurestatement · cited by 10
- Submonoid.closure_unionstatement · cited by 10
- Submonoid.map_powersproof · cited by 10
- Subgroup.closure_toSubmonoidstatement and proof · cited by 9