Theorems · Theorem · nonassociative algebras
leibniz_lie
∀ {L₁ : Type u_1} {L₂ : Type u_2} {M : Type u_3} [inst : Bracket L₁ L₂] [inst_1 : Bracket L₁ M] [inst_2 : Bracket L₂ M]
[inst_3 : Add M] [IsLieTower L₁ L₂ M] (x : L₁) (y : L₂) (m : M), ⁅x, ⁅y, m⁆⁆ = ⁅⁅x, y⁆, m⁆ + ⁅y, ⁅x, m⁆⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bracket.bracketstatement · cited by 642
- Bracketstatement and proof · cited by 8
- IsLieTowerstatement and proof · cited by 4
- IsLieTower.leibniz_lieproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- LieSubmodule.lieIdeal_oper_eq_linear_spanproof · cited by 9
- lie_lieproof · cited by 8
- IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_fproof · cited by 3
- IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_fproof · cited by 3
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- IsSl2Triple.lie_h_pow_toEnd_eproof · cited by 1
- LieModule.Cohomology.d₂₃_comp_d₁₂proof · cited by 0
- lie_swap_lieproof · cited by 0