Theorems · Theorem · group theory
Submonoid.closure_eq
∀ {M : Type u_1} [inst : MulOneClass M] (S : Submonoid M), Submonoid.closure ↑S = SClosure of a submonoid S equals S.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, 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.
- SetLike.coestatement · cited by 8,199
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement · cited by 167
- GaloisInsertion.l_u_eqproof · cited by 37
- Submonoid.giproof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.splits_iff_exists_multiset'proof · cited by 4
- Submonoid.mem_iSup_of_directedproof · cited by 3
- Submonoid.closure_univproof · cited by 2
- Monoid.Coprod.mrange_inl_sup_mrange_inrproof · cited by 2
- Submonoid.fg_of_divisiveproof · cited by 2
- Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoinproof · cited by 2
- Submonoid.adjoin_eq_span_of_eq_spanproof · cited by 1
- MonoidWithZeroHom.valueMonoid_eq_valueGroupproof · cited by 1
- Submonoid.iSup_eq_closureproof · cited by 1
- Field.span_map_pow_expChar_pow_eq_top_of_isSeparableproof · cited by 0
- MonoidWithZeroHom.valueMonoid_eq_closureproof · cited by 0
- Submonoid.sup_eq_closureproof · cited by 0