Theorems · Theorem · group theory
Submonoid.closure_union
∀ {M : Type u_1} [inst : MulOneClass M] (s t : Set M),
Submonoid.closure (s ∪ t) = Submonoid.closure s ⊔ Submonoid.closure t- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 10 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.
Cites7
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
- Submonoidstatement · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- Submonoid.closurestatement · cited by 167
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_supproof · cited by 81
- Submonoid.giproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.splits_iff_exists_multiset'proof · cited by 4
- Algebra.adjoin_union_coe_submoduleproof · cited by 3
- Monoid.Coprod.mrange_inl_sup_mrange_inrproof · cited by 2
- Subgroup.toSubmonoid_zpowersproof · cited by 1
- MonoidWithZeroHom.valueMonoid_eq_valueGroupproof · cited by 1
- Submonoid.FG.prodproof · cited by 1
- Submonoid.FG.supproof · cited by 1
- Submonoid.closure_insert_oneproof · cited by 0
- Submonoid.mem_closure_pairproof · cited by 0
- Submonoid.sup_eq_closureproof · cited by 0