Theorems · Theorem · group theory
Subgroup.mem_sup_left
∀ {G : Type u_1} [inst : Group G] {S T : Subgroup G} {x : G}, x ∈ S → x ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 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.
Cites3
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
- le_sup_leftproof · cited by 265
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.mul_mem_supproof · cited by 6
- MulAction.IwasawaStructure.commutator_leproof · cited by 4
- SL2Gen.transvection_mem_lineStab_supproof · cited by 1
- MonoidHom.noncommCoprod_rangeproof · cited by 1