Theorems · Theorem · group theory
AddSubgroup.addCommutator_le
∀ {G : Type u_1} [inst : AddGroup G] {H₁ H₂ H₃ : AddSubgroup G}, ⁅H₁, H₂⁆ ≤ H₃ ↔ ∀ g₁ ∈ H₁, ∀ g₂ ∈ H₂, ⁅g₁, g₂⁆ ∈ H₃- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 70 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketstatement and proof · cited by 642
- addCommutatorElementstatement · cited by 35
- AddSubgroup.closure_leproof · cited by 30
Cited by11
Results whose statement or proof uses this declaration.
- AddSubgroup.addCommutator_eq_bot_iff_le_centralizerproof · cited by 7
- AddSubgroup.addCommutator_monoproof · cited by 7
- AddSubgroup.map_addCommutatorproof · cited by 6
- AddSubgroup.addCommutator_le_rightproof · cited by 4
- AddSubgroup.addCommutator_pi_pi_leproof · cited by 2
- AddSubgroup.addCommutator_top_left_le_iffproof · cited by 2
- AddSubgroup.le_normalizer_iff_addCommutator_le_rightproof · cited by 1
- AddSubgroup.addCommutator_comm_leproof · cited by 1
- AddSubgroup.addCommutator_sum_sumproof · cited by 1
- AddSubgroup.addCommutator_addCommutator_eq_bot_of_rotateproof · cited by 1
- AddSubgroup.addCommutator_le_supproof · cited by 0