Theorems · Theorem · nonassociative algebras
lie_mem_left
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L) (x y : L), x ∈ I → ⁅x, y⁆ ∈ I
- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement · cited by 642
- LieIdealstatement and proof · cited by 282
- lie_skewproof · cited by 26
- neg_lieproof · cited by 4
- lie_mem_rightproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- LieIdeal.corootSubmodule_leproof · cited by 4
- LieAlgebra.InvariantForm.orthogonal_disjointproof · cited by 3
- LieIdeal.rootSpace_le_of_apply_coroot_ne_zeroproof · cited by 2
- LieIdeal.root_apply_eq_zero_of_notMem_rootSetproof · cited by 2
- LieIdeal.isCompl_killingComplproof · cited by 0
- LieAlgebra.IsSemisimple.isSimple_of_isAtomproof · cited by 0