Theorems · Theorem · group theory
Subgroup.mem_closure_of_mem
∀ {G : Type u_1} [inst : Group G] {s : Set G} {x : G}, x ∈ s → x ∈ Subgroup.closure s- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 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.
Cites5
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Subgroup.closurestatement · cited by 196
- Subgroup.subset_closureproof · cited by 53
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.le_normalizer_closure_iffproof · cited by 1
- Group.fg_of_descentproof · cited by 1
- SlashInvariantForm.slash_action_generatorsproof · cited by 1