Theorems · Theorem · nonassociative algebras
LieRingModule.lie_add
∀ {L : Type v} {M : Type w} {inst : LieRing L} {inst_1 : AddCommGroup M} [self : LieRingModule L M] (x : L) (m n : M),
⁅x, m + n⁆ = ⁅x, m⁆ + ⁅x, n⁆A Lie ring module bracket is additive in its second component.
- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- LieRingModule
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.
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement · cited by 642
Cited by2
Results whose statement or proof uses this declaration.
- lie_addproof · cited by 19
- LieRingModule.toEndproof · cited by 3