Theorems · Theorem · group theory
AddSubmonoid.closure_singleton_eq
∀ {A : Type u_2} [inst : AddMonoid A] (x : A), AddSubmonoid.closure {x} = AddMonoidHom.mrange ((multiplesHom A) x)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- Set.singleton_subset_iffproof · cited by 206
- Set.mem_singletonproof · cited by 183
- AddSubmonoid.subset_closureproof · cited by 63
- one_nsmulproof · cited by 63
- AddMonoidHom.mrangestatement and proof · cited by 61
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.mem_closure_singletonproof · cited by 2
- AddSubmonoid.one_eq_closureproof · cited by 1