Theorems · Theorem · group theory
AddSubgroup.sup_eq_closure
∀ {G : Type u_1} [inst : AddGroup G] (H H' : AddSubgroup G), H ⊔ H' = AddSubgroup.closure (↑H ∪ ↑H')- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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 · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.closurestatement · cited by 156
- AddSubgroup.closure_eqproof · cited by 7
- AddSubgroup.closure_unionproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_supproof · cited by 4
- AddSubgroup.mem_sup_of_normal_rightproof · cited by 1