Theorems · Definition · group theory
AddSubmonoid.closure
{M : Type u_1} → [inst : AddZeroClass M] → Set M → AddSubmonoid MThe AddSubmonoid generated by a set
- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 224 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 66 definitions · uses propext, Quot.sound
- Assumes
- AddZeroClass
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
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- InfSet.sInfproof · cited by 935
Cited by242
Results whose statement or proof uses this declaration.
- AddSubmonoid.subset_closurestatement · cited by 63
- AddSubmonoid.FGproof · cited by 36
- AddSubmonoid.closure_lestatement · cited by 35
- AddSubmonoid.closure_inductionstatement and proof · cited by 30
- IsLinearSetproof · cited by 28
- AddMonoidHom.map_mclosurestatement · cited by 12
- AddSubmonoid.closure_eqstatement · cited by 10
- AddSubmonoid.closure_monostatement · cited by 10
- AddSubmonoid.closure_unionstatement · cited by 10
- IsProperLinearSetproof · cited by 9
- AddSubmonoid.mem_closurestatement · cited by 8
- star_le_star_iffproof · cited by 6
Showing the 200 most cited of 242.