Theorems · Theorem · group theory
AddSubgroup.closure_eq_top_of_mclosure_eq_top
∀ {G : Type u_1} [inst : AddGroup G] {S : Set G}, AddSubmonoid.closure S = ⊤ → AddSubgroup.closure S = ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 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.
Cites9
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
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- AddSubgroup.closurestatement and proof · cited by 156
- AddSubgroup.eq_top_iff'proof · cited by 11
- AddSubgroup.le_closure_toAddSubmonoidproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.closure_range_inl_union_inrproof · cited by 1