Theorems · Theorem · nonassociative algebras
LieSubmodule.lie_comm
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I J : LieIdeal R L),
⁅I, J⁆ = ⁅J, I⁆- Defined in
- Mathlib.Algebra.Lie.IdealOperations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- le_antisymmproof · cited by 2,068
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement and proof · cited by 642
- LieSubmoduleproof · cited by 489
- LieIdealstatement and proof · cited by 282
- lie_skewproof · cited by 26
- LieSubmodule.lieSpan_leproof · cited by 17
- LieSubmodule.lieIdeal_oper_eq_spanproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- LieSubmodule.lie_le_leftproof · cited by 4