Theorems · Theorem · group theory
AddSubgroup.addCommutator_top_left_le_iff
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, ⁅⊤, H⁆ ≤ H ↔ H.Normal- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 2 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Bracket.bracketstatement and proof · cited by 642
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.neg_memproof · cited by 23
- AddSubgroup.addCommutator_leproof · cited by 11
- AddSubgroup.add_mem_cancel_rightproof · cited by 6
- AddSubgroup.addCommutator_le_rightproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.addCommutator_top_right_le_iffproof · cited by 0
- AddSubgroup.Normal.of_addCommutator_leproof · cited by 0