Theorems · Theorem · group theory
Subgroup.commutator_le_left
∀ {G : Type u_1} [inst : Group G] (H₁ H₂ : Subgroup G) [H₁.Normal], ⁅H₁, H₂⁆ ≤ H₁- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Bracket.bracketstatement · cited by 642
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.commutator_commproof · cited by 7
- Subgroup.commutator_le_rightproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.commutator_bot_leftproof · cited by 2
- Subgroup.commutator_le_infproof · cited by 1