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Theorems · Theorem · nonassociative algebras

lie_mem_right

∀ (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), y ∈ I → ⁅x, y⁆ ∈ I
Defined in
Mathlib.Algebra.Lie.Ideal
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
CommRingLieRingLieAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

lie_mem_left · cited by 6lie_mem_leftLieAlgebra.IsSemisimple.isSimple_of_isAtom · cited by 0IsSemisimple.isSimple_of_…CommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraBracket.bracket · cited by 642Bracket.bracketLieIdeal · cited by 282LieIdealLieSubmodule.lie_mem · cited by 23LieSubmodule.lie_memlie_mem_rightCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.