Theorems · Theorem · group theory
Subgroup.closure_eq_of_le
∀ {G : Type u_1} [inst : Group G] (K : Subgroup G) {k : Set G}, k ⊆ ↑K → K ≤ Subgroup.closure k → Subgroup.closure k = K- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 4 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.
Cites7
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- le_antisymmproof · cited by 2,068
- Subgroup.closurestatement and proof · cited by 196
- Subgroup.closure_leproof · cited by 31
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.closure_three_cycles_eq_alternatingproof · cited by 3
- RootPairing.range_weylGroupToPermproof · cited by 0
- RootPairing.range_weylGroup_coweightHomproof · cited by 0
- RootPairing.range_weylGroup_weightHomproof · cited by 0