Theorems · Theorem · group theory
AddSubgroup.le_normalizer_iff_addCommutator_le_right
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, H ≤ AddSubgroup.normalizer ↑K ↔ ⁅H, K⁆ ≤ K- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketstatement and proof · cited by 642
- AddMemClass.add_memproof · cited by 229
- NegMemClass.neg_memproof · cited by 63
- AddSubgroup.normalizerstatement · cited by 59
- AddSubgroup.addCommutator_leproof · cited by 11
- add_mem_cancel_rightproof · cited by 10
- AddSubgroup.addCommutator_mem_addCommutatorproof · cited by 9
- AddSubgroup.le_normalizer_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.le_normalizer_iff_addCommutator_le_leftproof · cited by 1