Theorems · Theorem · group theory
AddSubgroup.closure_add_le
∀ {G : Type u_2} [inst : AddGroup G] (S T : Set G),
AddSubgroup.closure (S + T) ≤ AddSubgroup.closure S ⊔ AddSubgroup.closure T- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 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.
Cites12
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
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Set.addstatement · cited by 338
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- AddSubgroup.closurestatement and proof · cited by 156
- sInf_leproof · cited by 110
- SetLike.le_defproof · cited by 76
- AddSubgroup.subset_closureproof · cited by 49
- AddSubgroup.add_memproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.sup_eq_closure_addproof · cited by 1