Theorems · Theorem · nonassociative algebras

lie_swap_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 : Bracket L₂ L₁] [inst_4 : AddCommGroup M] [IsLieTower L₁ L₂ M] [IsLieTower L₂ L₁ M] (x : L₁) (y : L₂)
  (m : M), ⁅⁅x, y⁆, m⁆ = -⁅⁅y, x⁆, m⁆

Defined in: Mathlib.Algebra.Lie.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 13 from the axioms · uses propext
Assumes: Bracket Bracket Bracket Bracket AddCommGroup IsLieTower IsLieTower

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AddCommGroupstatement and proof · cited by 12,871
Bracket.bracketstatement and proof · cited by 642
add_sub_cancel_rightproof · cited by 187
sub_add_cancel_rightproof · cited by 17
leibniz_lieproof · cited by 8
Bracketstatement and proof · cited by 8
IsLieTowerstatement and proof · cited by 4

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