Theorems · Theorem · group theory
AddSubgroup.addCommutator_sum_sum
∀ {G : Type u_1} {G' : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup G'] (H₁ H₂ : AddSubgroup G)
(K₁ K₂ : AddSubgroup G'), ⁅H₁.prod K₁, H₂.prod K₂⁆ = ⁅H₁, H₂⁆.prod ⁅K₁, K₂⁆- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_antisymmproof · cited by 2,068
- Bracket.bracketstatement and proof · cited by 642
- bot_leproof · cited by 306
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddMonoidHom.sndproof · cited by 42
- AddMonoidHom.fstproof · cited by 39
- AddSubgroup.prodstatement and proof · cited by 34
- AddMonoidHom.inlproof · cited by 29
- AddMonoidHom.inrproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.lowerCentralSeries_sumproof · cited by 1