Theorems · Theorem · nonassociative algebras
add_lie
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (x y : L) (m : M),
⁅x + y, m⁆ = ⁅x, m⁆ + ⁅y, m⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LieRingModule.add_lieproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- lie_skewproof · cited by 26
- zero_lieproof · cited by 16
- sub_lieproof · cited by 5
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- neg_lieproof · cited by 4
- LieSubmodule.lie_baseChangeproof · cited by 3
- LieAlgebra.Basis.baseSupp_apply_smul_eproof · cited by 3
- LieSubmodule.sup_lieproof · cited by 1
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zeroproof · cited by 1
- LieSubalgebra.lie_mem_sup_of_mem_normalizerproof · cited by 1
- nsmul_lieproof · cited by 1