Theorems · Theorem · nonassociative algebras
lie_add
∀ {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
- 19 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.lie_addproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- LieModule.toEndproof · cited by 144
- lie_skewproof · cited by 26
- lie_zeroproof · cited by 18
- LieSubmodule.lieIdeal_oper_eq_linear_spanproof · cited by 9
- lie_negproof · cited by 5
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- LieSubmodule.lie_baseChangeproof · cited by 3
- LieModule.lie_mem_genWeightSpaceChain_of_genWeightSpace_eq_bot_rightproof · cited by 2
- LieSubmodule.lie_supproof · cited by 2
- lie_subproof · cited by 2
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zeroproof · cited by 1