Theorems · Theorem · group theory
Subgroup.mul_mem_sup
∀ {G : Type u_1} [inst : Group G] {S T : Subgroup G} {x y : G}, x ∈ S → y ∈ T → x * y ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mul_memproof · cited by 30
- Subgroup.mem_sup_leftproof · cited by 4
- Subgroup.mem_sup_rightproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.comap_map_eqproof · cited by 9
- NumberField.Units.closure_fundSystem_sup_torsion_eq_topproof · cited by 2
- Subgroup.mem_supproof · cited by 2
- Subgroup.IsComplement'.isComplproof · cited by 2
- Sylow.normalizer_sup_eq_topproof · cited by 2
- Subgroup.mem_sup_of_normal_rightproof · cited by 1