Theorems · Theorem · group theory
AddSubgroup.add_mem_sup
∀ {G : Type u_1} [inst : AddGroup G] {S T : AddSubgroup G} {x y : G}, x ∈ S → y ∈ T → x + y ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.add_memproof · cited by 17
- AddSubgroup.mem_sup_rightproof · cited by 1
- AddSubgroup.mem_sup_leftproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.comap_map_eqproof · cited by 8
- AddSubgroup.mem_supproof · cited by 4
- AddSubgroup.mem_sup_of_normal_rightproof · cited by 1