Theorems · Theorem · group theory
AddSubgroup.le_closure_toAddSubmonoid
∀ {G : Type u_1} [inst : AddGroup G] (S : Set G), AddSubmonoid.closure S ≤ (AddSubgroup.closure S).toAddSubmonoid- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 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.
Cites8
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
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement · cited by 224
- AddSubgroup.closurestatement · cited by 156
- AddSubgroup.toAddSubmonoidstatement · cited by 91
- AddSubgroup.subset_closureproof · cited by 49
- AddSubmonoid.closure_leproof · cited by 35
Cited by5
Results whose statement or proof uses this declaration.
- topologicalClosure_addSubgroupClosure_toAddSubmonoidproof · cited by 1
- AddSubgroup.closure_eq_top_of_mclosure_eq_topproof · cited by 1
- AddSubgroup.closure_image_isAddIndecomposable_baseOfproof · cited by 1
- RootPairing.ncard_eq_finrank_of_linearIndepOn_ofproof · cited by 1
- AddSubgroup.closure_toAddSubmonoid_of_isOfFinAddOrderproof · cited by 1