Theorems · Theorem · nonassociative algebras
LieRingModule.add_lie
∀ {L : Type v} {M : Type w} {inst : LieRing L} {inst_1 : AddCommGroup M} [self : LieRingModule L M] (x y : L) (m : M),
⁅x + y, m⁆ = ⁅x, m⁆ + ⁅y, m⁆A Lie ring module bracket is additive in its first 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 by1
Results whose statement or proof uses this declaration.
- add_lieproof · cited by 20