Theorems · Definition · nonassociative algebras
Bracket.bracket
{L : Type u_1} → {M : Type u_2} → [self : Bracket L M] → L → M → M⁅x, y⁆ is the result of a bracket operation on elements x and y.
It is supported by the Bracket typeclass.
- Defined in
- Mathlib.Data.Bracket
- Cited by
- 642 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Bracket
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bracketstatement and proof · cited by 8
Cited by748
Results whose statement or proof uses this declaration.
- LieModule.toEndproof · cited by 144
- commutatorproof · cited by 56
- LieModule.toEnd_apply_applystatement · cited by 39
- LieAlgebra.derivedSeriesOfIdealproof · cited by 28
- lie_skewstatement and proof · cited by 26
- LieModule.lowerCentralSeries_succstatement · cited by 26
- LieModule.maxTrivSubmoduleproof · cited by 25
- LieSubmodule.lie_memstatement · cited by 23
- LieSubmodule.normalizerproof · cited by 21
- commutatorSetproof · cited by 20
- add_liestatement · cited by 20
- lie_addstatement · cited by 19
Showing the 200 most cited of 748.