Theorems · Theorem · group theory
AddSubgroup.addCommutator_comm
∀ {G : Type u_1} [inst : AddGroup G] (H₁ H₂ : AddSubgroup G), ⁅H₁, H₂⁆ = ⁅H₂, H₁⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_antisymmproof · cited by 2,068
- Bracket.bracketstatement · cited by 642
- AddSubgroup.addCommutator_comm_leproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- AddSubgroup.addCommutator_le_leftproof · cited by 2
- AddSubgroup.normalizer_addCommutator_ge_rightproof · cited by 1
- AddSubgroup.le_normalizer_iff_addCommutator_le_leftproof · cited by 1
- AddSubgroup.addCommutator_top_right_le_iffproof · cited by 0
- AddSubgroup.addCommutator_top_left_eq_bot_iff_le_centerproof · cited by 0
- addCommutator_centralizer_addCommutator_le_centerproof · cited by 0