Theorems · Theorem · group theory
Subgroup.commutator_top_left_le_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, ⁅⊤, H⁆ ≤ H ↔ H.Normal- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Bracket.bracketstatement and proof · cited by 642
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.inv_memproof · cited by 40
- Subgroup.commutator_leproof · cited by 10
- Subgroup.mul_mem_cancel_rightproof · cited by 7
- Subgroup.commutator_le_rightproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.commutator_top_right_le_iffproof · cited by 0
- Subgroup.Normal.of_commutator_leproof · cited by 0