Theorems · Theorem · nonassociative algebras
lie_sub
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (x : L) (m n : M),
⁅x, m - n⁆ = ⁅x, m⁆ - ⁅x, n⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- sub_eq_add_negproof · cited by 1,023
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement and proof · cited by 642
- lie_addproof · cited by 19
- lie_negproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplittingproof · cited by 0
- LieModule.Cohomology.d₂₃_comp_d₁₂proof · cited by 0