Theorems · Theorem · group theory
AddSubgroup.closure_union
∀ {G : Type u_1} [inst : AddGroup G] (s t : Set G),
AddSubgroup.closure (s ∪ t) = AddSubgroup.closure s ⊔ AddSubgroup.closure t- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.closurestatement · cited by 156
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_supproof · cited by 81
- AddSubgroup.giproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.range_inl_sup_range_inrproof · cited by 2
- AddSubgroup.closure_insert_zeroproof · cited by 2
- AddSubgroup.sup_eq_closureproof · cited by 2
- AddSubgroup.normalClosure_unionproof · cited by 1
- AddSubgroup.FG.supproof · cited by 1
- AddCircle.denseRange_zsmul_coe_iffproof · cited by 0
- AddSubgroup.mem_closure_pairproof · cited by 0