Theorems · Theorem · ring theory
Ring.lie_def
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] (x y : R), ⁅x, y⁆ = x * y - y * x- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bracket.bracketstatement · cited by 642
- NonUnitalNonAssocRingstatement and proof · cited by 354
Cited by5
Results whose statement or proof uses this declaration.
- LinearMap.trace_lieproof · cited by 3
- RootPairing.GeckConstruction.lie_h_fproof · cited by 1
- LieAlgebra.commute_ad_of_commuteproof · cited by 1
- RootPairing.GeckConstruction.lie_e_f_mul_ωproof · cited by 0
- LieModule.trace_toEnd_mul_eq_zero_of_traceForm_eq_zeroproof · cited by 0