Theorems · Theorem · group theory
Set.addSubgroupClosure_add
∀ {G : Type u_2} [inst : AddGroup G] {s : Set G}, s.Nonempty → ↑(AddSubgroup.closure s) + s = ↑(AddSubgroup.closure s)- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites15
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.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Set.Nonemptystatement and proof · cited by 2,627
- Set.iUnionproof · cited by 2,483
- HVAdd.hVAddproof · cited by 1,820
- Set.iUnion_congr_Propproof · cited by 374
- Set.addstatement · cited by 338
- AddOpposite.opproof · cited by 192
- AddSubgroup.closurestatement and proof · cited by 156
- AddSubgroup.subset_closureproof · cited by 49
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