Theorems · Theorem · group theory
AddSubgroup.addCommutator_mono
∀ {G : Type u_1} [inst : AddGroup G] {H₁ H₂ K₁ K₂ : AddSubgroup G}, H₁ ≤ K₁ → H₂ ≤ K₂ → ⁅H₁, H₂⁆ ≤ ⁅K₁, K₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 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
- Bracket.bracketstatement · cited by 642
- AddSubgroup.addCommutator_leproof · cited by 11
- AddSubgroup.addCommutator_mem_addCommutatorproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.lowerCentralSeries_monoproof · cited by 5
- AddSubgroup.lowerCentralSeries_pi_leproof · cited by 1
- AddSubgroup.addCommutator_pi_pi_of_finiteproof · cited by 1
- AddSubgroup.addCommutator_sum_sumproof · cited by 1
- addCommutator_centralizer_addCommutator_le_centerproof · cited by 0
- AddSubgroup.addCommutator_le_map_addCommutatorproof · cited by 0
- AddSubgroup.Normal.of_addCommutator_leproof · cited by 0