Theorems · Theorem · group theory
Subgroup.focalSubgroup_le
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H.focalSubgroup ≤ HLemma: The focal subgroup is indeed a subgroup of H.
- Defined in
- Mathlib.GroupTheory.Focal
- Cited by
- 2 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.
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketproof · cited by 642
- Subgroup.closure_leproof · cited by 31
- Subgroup.focalSubgroupstatement · cited by 9
- Subgroup.focalSubgroup_defproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.map_focalSubgroupOfproof · cited by 3
- Subgroup.commutator_inf_eq_focalSubgroupproof · cited by 0