Theorems · Theorem · group theory
Subsemigroup.closure_eq
∀ {M : Type u_1} [inst : Mul M] (S : Subsemigroup M), Subsemigroup.closure ↑S = SClosure of a subsemigroup S equals S.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, 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.
- SetLike.coestatement · cited by 8,199
- Subsemigroupstatement and proof · cited by 323
- Subsemigroup.closurestatement · cited by 43
- GaloisInsertion.l_u_eqproof · cited by 37
- Subsemigroup.giproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Subsemigroup.mem_iSup_of_directedproof · cited by 3
- Subsemigroup.iSup_eq_closureproof · cited by 1
- Subsemigroup.closure_univproof · cited by 0