Theorems · Definition · group theory
Subsemigroup.closure
{M : Type u_1} → [inst : Mul M] → Set M → Subsemigroup MThe Subsemigroup generated by a set.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- InfSet.sInfproof · cited by 935
- Subsemigroupstatement and proof · cited by 323
Cited by46
Results whose statement or proof uses this declaration.
- Subsemigroup.subset_closurestatement · cited by 16
- Subsemigroup.closure_lestatement · cited by 13
- Subsemigroup.closure_inductionstatement and proof · cited by 6
- Subsemigroup.gistatement · cited by 5
- Subsemigroup.mem_closurestatement · cited by 3
- Subsemigroup.closure_eqstatement · cited by 3
- Subsemigroup.mem_iSup_of_directedproof · cited by 3
- Submonoid.closure_eq_one_unionstatement and proof · cited by 2
- Subsemigroup.closure_iUnionstatement · cited by 2
- NonUnitalAlgebra.adjoin_eq_spanstatement and proof · cited by 2
- StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_spanproof · cited by 2
- NonUnitalSubsemiring.mem_closure_iffstatement · cited by 1